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Journal articles on the topic 'Computational stability analysis'

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Author: Grafiati

Published: 10 December 2022

Last updated: 28 January 2023

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1

Zhu, Zhi-Qiang, and Sui Sun Cheng. "Stability analysis for multistep computational schemes." Computers & Mathematics with Applications 55, no. 12 (June 2008): 2753–61. http://dx.doi.org/10.1016/j.camwa.2007.10.024.

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2

Huang, Qi Wu, Cang Qin Jia, Bo Ru Xia, and Gui He Wang. "Novel Computational Implementations for Stability Analysis." Applied Mechanics and Materials 90-93 (September 2011): 778–85. http://dx.doi.org/10.4028/www.scientific.net/amm.90-93.778.

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By exploring the nature of the analogy between optimum trusses and optimum layouts of discontinuities, a novel numerical analysis method for rock/soil masses is proposed in this paper. The procedure is used to determine the critical layout of discontinuities and associated upper bound limit analysis for stability problems. The alternative approximation procedure to the traditional finite element method might involve discretization of a given body using a suitably large number of nodes laid out on a grid, with the failure mechanism comprising the most critical subset of potential discontinuities interconnecting these nodes. Potential discontinuities which interlink nodes laid out across the problem domain are permitted to crossover one another, giving a much wider search space than when such discontinuities are located only at the edges of finite elements of fixed topology. Highly efficient SOCP (second-order cone programming) solvers can be employed when certain popular failure criteria are specified (e.g. Hoek-Brown and Mohr-Coulomb). Stress/velocity singularities are automatically identified and visual interpretation of the output is straightforward. Several numerical examples including rock slope are studied by the new method, and the results are very close to those calculated by using analytical method and FEM.

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3

Wu, Zhou, Liu Zhijun, and Tang Lifang. "Computational Analysis of the Slope Stability of Flood Prevention and Bank Protection Engineering." International Journal of Engineering and Technology 8, no. 2 (February 2016): 137–40. http://dx.doi.org/10.7763/ijet.2016.v6.873.

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4

Wu, Zhou, Liu Zhijun, and Tang Lifang. "Computational Analysis of the Slope Stability of Flood Prevention and Bank Protection Engineering." International Journal of Engineering and Technology 8, no. 2 (February 2016): 137–40. http://dx.doi.org/10.7763/ijet.2016.v8.873.

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5

Luyckx, L., M. Loccufier, and E. Noldus. "Computational methods in nonlinear stability analysis: stability boundary calculations." Journal of Computational and Applied Mathematics 168, no. 1-2 (July 2004): 289–97. http://dx.doi.org/10.1016/j.cam.2003.05.021.

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6

Polcz, Péter. "Computational Stability Analysis of Lotka-Volterra Systems." Hungarian Journal of Industry and Chemistry 44, no. 2 (December 1, 2016): 113–20. http://dx.doi.org/10.1515/hjic-2016-0014.

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Abstract This paper concerns the computational stability analysis of locally stable Lotka-Volterra (LV) systems by searching for appropriate Lyapunov functions in a general quadratic form composed of higher order monomial terms. The Lyapunov conditions are ensured through the solution of linear matrix inequalities. The stability region is estimated by determining the level set of the Lyapunov function within a suitable convex domain. The paper includes interesting computational results and discussion on the stability regions of higher (3,4) dimensional LV models as well as on the monomial selection for constructing the Lyapunov functions. Finally, the stability region is estimated of an uncertain 2D LV system with an uncertain interior locally stable equilibrium point.

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7

Chen, S. G., A. G. Ulsoy, and Y. Koren. "Computational Stability Analysis of Chatter in Turning." Journal of Manufacturing Science and Engineering 119, no. 4A (November 1, 1997): 457–60. http://dx.doi.org/10.1115/1.2831174.

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Machine tool chatter is one of the major constraints that limits productivity of the turning process. It is a self-excited vibration that is mainly caused by the interaction between the machine-tool/workpiece structure and the cutting process dynamics. This work introduces a general method which avoids lengthy algebraic (symbolic) manipulations in deriving, a characteristic equation. The solution scheme is simple and robust since the characteristic equation is numerically formulated as a single variable equation whose variable is well bounded rather than two nonlinear algebraic equations with unbounded variables. An asymptotic stability index is also introduced for a relative stability analysis. The method can be applied to other machining processes, as long as the system equations can be expressed as a set of linear time invariant difference-differential equations.

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8

Yim, Solomon C. S., Tongchate Nakhata, and Erick T. Huang. "Coupled Nonlinear Barge Motions, Part II: Stochastic Models and Stability Analysis." Journal of Offshore Mechanics and Arctic Engineering 127, no. 2 (May 1, 2005): 83–95. http://dx.doi.org/10.1115/1.1884617.

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A computationally efficient quasi-two-degree-of-freedom (Q2DOF) stochastic model and a stability analysis of barges in random seas are presented in this paper. Based on the deterministic 2DOF coupled roll-heave model with high-degree polynomial approximation of restoring forces and moments developed in Part I, an attempt is made to further reduce the DOF of the model for efficient stochastic stability analysis by decoupling the heave effects on roll motion, resulting in a one-degree-of-freedom (1DOF) roll-only model. Using the Markov assumption, stochastic differential equations governing the evolution of probability densities of roll-heave and roll responses for the two low-DOF models are derived via the Fokker-Planck formulation. Numerical results of roll responses for the 2DOF and 1DOF models, using direct simulation in the time domain and the path integral solution technique in the probability domain, are compared to determine the effects of neglecting the influence of heave on roll motion and assess the relative computational efforts required. It is observed that the 1DOF model is computationally very efficient and the 2DOF model response predictions are quite accurate. However, the nonlinear roll-heave coupling is found to be significant and needs to be directly taken into account, rendering the 1DOF roll-only model inadequate for practical use. The 2DOF model is impractical for long-duration real-time response computation due to the insurmountable computational effort required. By taking advantage of the observed strong correlation between measured heave and wave elevation in the experimental results, an accurate and efficient Q2DOF model is developed by expressing the heave response in the 2DOF model as a function of wave elevation, thus reducing the effective DOF to unity. This Q2DOF model is essential as it reduces the computational effort by a factor of 10−5 compared to that of the 2DOF model, thus making practical stochastic analysis possible. A stochastic stability analysis of the barge under operational and survival sea states specified by the U.S. Navy is presented using the Q2DOF model based on first passage time formulation.

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9

Jafri, M., Iswan Iswan, M. Rizki, and G. Susilo. "Slope stability analysis in Ulubelu Lampung using computational analysis program." Civil and Environmental Science 003, no. 01 (April 1, 2020): 051–59. http://dx.doi.org/10.21776/ub.civense.2020.00301.6.

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10

Gerecht, D., R. Rannacher, and W. Wollner. "Computational Aspects of Pseudospectra in Hydrodynamic Stability Analysis." Journal of Mathematical Fluid Mechanics 14, no. 4 (November 29, 2011): 661–92. http://dx.doi.org/10.1007/s00021-011-0085-7.

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11

Yeo, Hyeonsoo, Mark Potsdam, and Robert A. Ormiston. "Rotor Aeroelastic Stability Analysis Using Coupled Computational Fluid Dynamics/Computational Structural Dynamics." Journal of the American Helicopter Society 56, no. 4 (October 1, 2011): 1–16. http://dx.doi.org/10.4050/jahs.56.042003.

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Computational fluid dynamics/computational structural dynamics (CFD/CSD) coupling was successfully applied to the rotor aeroelastic stability problem to calculate lead–lag regressing mode damping of a hingeless rotor in hover and forward flight. A direct time domain numerical integration of the equations in response to suitable excitation was solved using a tight CFD/CSD coupling. Two different excitation methods—swashplate cyclic pitch and blade tip lead–lag force excitations—were investigated to provide suitable blade transient responses. The free decay transient response time histories were postprocessed using the moving-block method to determine the damping as a function of the rotor operating conditions. Coupled CFD/CSD analysis results are compared with the experimentally measured stability data obtained for a 7.5-ft-diameter Mach-scale hingeless rotor model as well as stability predictions using the comprehensive analysis Rotorcraft Comprehensive Analysis System (RCAS). The coupled CFD/CSD predictions agreed more closely with the experimental lead–lag damping measurements than RCAS predictions based on conventional aerodynamic methods, better capturing key features in the damping trends.

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12

Tutueva, Aleksandra, and Denis Butusov. "Stability Analysis and Optimization of Semi-Explicit Predictor–Corrector Methods." Mathematics 9, no. 19 (October 3, 2021): 2463. http://dx.doi.org/10.3390/math9192463.

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The increasing complexity of advanced devices and systems increases the scale of mathematical models used in computer simulations. Multiparametric analysis and study on long-term time intervals of large-scale systems are computationally expensive. Therefore, efficient numerical methods are required to reduce time costs. Recently, semi-explicit and semi-implicit Adams–Bashforth–Moulton methods have been proposed, showing great computational efficiency in low-dimensional systems simulation. In this study, we examine the numerical stability of these methods by plotting stability regions. We explicitly show that semi-explicit methods possess higher numerical stability than the conventional predictor–corrector algorithms. The second contribution of the reported research is a novel algorithm to generate an optimized finite-difference scheme of semi-explicit and semi-implicit Adams–Bashforth–Moulton methods without redundant computation of predicted values that are not used for correction. The experimental part of the study includes the numerical simulation of the three-body problem and a network of coupled oscillators with a fixed and variable integration step and finely confirms the theoretical findings.

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13

Wang, Dehua, Xiao-Li Ding, and Juan J. Nieto. "Stability analysis of fractional-order systems with randomly time-varying parameters." Nonlinear Analysis: Modelling and Control 26, no. 3 (May 1, 2021): 440–60. http://dx.doi.org/10.15388/namc.2021.26.23053.

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This paper is concerned with the stability of fractional-order systems with randomly timevarying parameters. Two approaches are provided to check the stability of such systems in mean sense. The first approach is based on suitable Lyapunov functionals to assess the stability, which is of vital importance in the theory of stability. By an example one finds that the stability conditions obtained by the first approach can be tabulated for some special cases. For some complicated linear and nonlinear systems, the stability conditions present computational difficulties. The second alternative approach is based on integral inequalities and ingenious mathematical method. Finally, we also give two examples to demonstrate the feasibility and advantage of the second approach. Compared with the stability conditions obtained by the first approach, the stability conditions obtained by the second one are easily verified by simple computation rather than complicated functional construction. The derived criteria improve the existing related results.

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14

Sousa, Ercı́lia. "The controversial stability analysis." Applied Mathematics and Computation 145, no. 2-3 (December 2003): 777–94. http://dx.doi.org/10.1016/s0096-3003(03)00274-1.

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15

Xiao, Shuangshuang, Kemin Li, Xiaohua Ding, and Tong Liu. "Numerical Computation of Homogeneous Slope Stability." Computational Intelligence and Neuroscience 2015 (2015): 1–10. http://dx.doi.org/10.1155/2015/802835.

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To simplify the computational process of homogeneous slope stability, improve computational accuracy, and find multiple potential slip surfaces of a complex geometric slope, this study utilized the limit equilibrium method to derive expression equations of overall and partial factors of safety. This study transformed the solution of the minimum factor of safety (FOS) to solving of a constrained nonlinear programming problem and applied an exhaustive method (EM) and particle swarm optimization algorithm (PSO) to this problem. In simple slope examples, the computational results using an EM and PSO were close to those obtained using other methods. Compared to the EM, the PSO had a small computation error and a significantly shorter computation time. As a result, the PSO could precisely calculate the slope FOS with high efficiency. The example of the multistage slope analysis indicated that this slope had two potential slip surfaces. The factors of safety were 1.1182 and 1.1560, respectively. The differences between these and the minimum FOS (1.0759) were small, but the positions of the slip surfaces were completely different than the critical slip surface (CSS).

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16

Kanan, A., E. Polukhov, M. A. Keip, L. Dorfmann, and M. Kaliske. "Computational material stability analysis in finite thermo-electro-mechanics." Mechanics Research Communications 121 (April 2022): 103867. http://dx.doi.org/10.1016/j.mechrescom.2022.103867.

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17

Katagiri, Daisuke, Takahiro Tsuchiya, Minoru Tsuda, Masayuki Hata, and Tyuji Hoshino. "Computational Analysis of Stability of the β-Sheet Structure." Journal of Physical Chemistry B 106, no. 35 (September 2002): 9151–58. http://dx.doi.org/10.1021/jp025757m.

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18

Steiner, Juri A., Stephen J. Ferguson, and G. Harry van Lenthe. "Computational analysis of primary implant stability in trabecular bone." Journal of Biomechanics 48, no. 5 (March 2015): 807–15. http://dx.doi.org/10.1016/j.jbiomech.2014.12.008.

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19

Tulus, T. J. Marpaung, and J. L. Marpaung. "Computational Analysis for Dam Stability Against Water Flow Pressure." Journal of Physics: Conference Series 2421, no. 1 (January 1, 2023): 012013. http://dx.doi.org/10.1088/1742-6596/2421/1/012013.

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Abstract Fatigue analysis of an object’s structure is very important because it can provide a numerical value that can be used as a reference before acting. The finite element method is a numerical method that can calculate the value of the fatigue and stability of a structure by calculating the reynold value and the pressure given. This study aims to conduct a structural fatigue analysis of the dam that focuses on the Reynold value in order to provide an analysis and representation of the dam structure. The result to be achieved is a mathematical model that analyzes the fatigue of the dam structure by connecting the elevation angle, water velocity, time, and the force obtained from the kinetic energy in the water flow.

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20

Johnson, Claes, Rolf Rannacher, and Mats Boman. "Numerics and Hydrodynamic Stability: Toward Error Control in Computational Fluid Dynamics." SIAM Journal on Numerical Analysis 32, no. 4 (August 1995): 1058–79. http://dx.doi.org/10.1137/0732048.

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21

Barker, B., J. Humpherys, G. Lyng, and J. Lytle. "Evans function computation for the stability of travelling waves." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376, no. 2117 (March 5, 2018): 20170184. http://dx.doi.org/10.1098/rsta.2017.0184.

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In recent years, the Evans function has become an important tool for the determination of stability of travelling waves. This function, a Wronskian of decaying solutions of the eigenvalue equation, is useful both analytically and computationally for the spectral analysis of the linearized operator about the wave. In particular, Evans-function computation allows one to locate any unstable eigenvalues of the linear operator (if they exist); this allows one to establish spectral stability of a given wave and identify bifurcation points (loss of stability) as model parameters vary. In this paper, we review computational aspects of the Evans function and apply it to multidimensional detonation waves. This article is part of the theme issue ‘Stability of nonlinear waves and patterns and related topics’.

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22

Szweda, Jan, Zdenek Poruba, Roman Sikora, and Jiří Podešva. "Computational Analysis of Mechanism Operability." Applied Mechanics and Materials 315 (April 2013): 879–83. http://dx.doi.org/10.4028/www.scientific.net/amm.315.879.

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This article deals with a way of interpretation the results of numerical simulations solved for the mechanism of lifting platform. Subject of analysis is the atypical design solution of lifting mechanism with one degree of freedom, which members are connected by revolute joints and linear sliding guidance. The mechanism movement is provided by linear hydromotors. Computational simulations are carried out by FEM, where linear coupling equations are used for modeling of revolute joints and linear sliding guidance is modeled by structural contact of rail and slider. The way of modeling and parameters setting of structural contact significantly affects the stability of numerical solutions and the obtained results. The authors assume that the interpretation of the observed behavior and results of the numerical simulations allow to deduce the mechanism operability and gives a clue for setting the gap of real bounds.

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23

Sklyarova, Ekaterina V., Yuri M. Nechepurenko, and Gennady A. Bocharov. "Numerical steady state analysis of the Marchuk–Petrov model of antiviral immune response." Russian Journal of Numerical Analysis and Mathematical Modelling 35, no. 2 (April 28, 2020): 95–110. http://dx.doi.org/10.1515/rnam-2020-0008.

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Abstract The problem of guaranteed computation of all steady states of the Marchuk–Petrov model with fixed values of parameters and analysis of their stability are considered. It is shown that the system of ten nonlinear equations, nonnegative solutions of which are steady states, can be reduced to a system of two equations. The region of possible nonnegative solutions is analytically localized. An effective technology for computing all nonnegative solutions and analyzing their stability is proposed. The obtained results provide a computational basis for the study of chronic forms of viral infections using the Marchuk–Petrov model.

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24

Kuang, Zengtao, Qun Huang, Wei Huang, Jie Yang, Hamid Zahrouni, Michel Potier-Ferry, and Heng Hu. "A computational framework for multi-stability analysis of laminated shells." Journal of the Mechanics and Physics of Solids 149 (April 2021): 104317. http://dx.doi.org/10.1016/j.jmps.2021.104317.

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25

Azim Shaikh, Fouzul, Mr Zaheeruddin, and M. S Jamil Asghar. "Computational Intelligence and Voltage Stability Analysis for Mitigation of Blackout." International Journal of Computer Applications 16, no. 2 (February 28, 2011): 6–11. http://dx.doi.org/10.5120/1987-2677.

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26

Hunanyan, Areg A., Vladimir M. Aroutiounian, and Hayk A. Zakaryan. "Computational Search and Stability Analysis of Two-Dimensional Tin Oxides." Journal of Physical Chemistry C 126, no. 9 (February 24, 2022): 4647–54. http://dx.doi.org/10.1021/acs.jpcc.1c10252.

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27

Ghatage, Swapnil V., Zhengbiao Peng, Mayur J. Sathe, Elham Doroodchi, Nitin Padhiyar, Behdad Moghtaderi, Jyeshtharaj B. Joshi, and Geoffrey M. Evans. "Stability analysis in solid–liquid fluidized beds: Experimental and computational." Chemical Engineering Journal 256 (November 2014): 169–86. http://dx.doi.org/10.1016/j.cej.2014.06.026.

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28

Polukhov, E., D. Vallicotti, and M. A. Keip. "Computational stability analysis of periodic electroactive polymer composites across scales." Computer Methods in Applied Mechanics and Engineering 337 (August 2018): 165–97. http://dx.doi.org/10.1016/j.cma.2018.01.020.

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29

Ardestani, Marzieh M., Chen ZhenXian, Hessam Noori-Dokht, Mehran Moazen, and Zhongmin Jin. "Computational analysis of knee joint stability following total knee arthroplasty." Journal of Biomechanics 86 (March 2019): 17–26. http://dx.doi.org/10.1016/j.jbiomech.2019.01.029.

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30

Liu, Qunfeng. "Order-2 Stability Analysis of Particle Swarm Optimization." Evolutionary Computation 23, no. 2 (June 2015): 187–216. http://dx.doi.org/10.1162/evco_a_00129.

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Several stability analyses and stable regions of particle swarm optimization (PSO) have been proposed before. The assumption of stagnation and different definitions of stability are adopted in these analyses. In this paper, the order-2 stability of PSO is analyzed based on a weak stagnation assumption. A new definition of stability is proposed and an order-2 stable region is obtained. Several existing stable analyses for canonical PSO are compared, especially their definitions of stability and the corresponding stable regions. It is shown that the classical stagnation assumption is too strict and not necessary. Moreover, among all these definitions of stability, it is shown that our definition requires the weakest conditions, and additional conditions bring no benefit. Finally, numerical experiments are reported to show that the obtained stable region is meaningful. A new parameter combination of PSO is also shown to be good, even better than some known best parameter combinations.

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31

Clarke, James, and Antonio Filippone. "Unsteady Computational Analysis of Vehicle Passing." Journal of Fluids Engineering 129, no. 3 (August 19, 2006): 359–67. http://dx.doi.org/10.1115/1.2427085.

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This paper presents results of the simulation of two vehicles overtaking each other at highways conditions (30m∕s). The simulation was fully unsteady and tracks the maneuver for several body lengths from downstream to upstream. Different mesh strategies have been investigated and assessed. Structured methods with sliding planes have been found the most feasible. The results shown include the effects of relative speed and lateral separation. The passing maneuver is described in detail, and a number of physical phenomena are identified. In particular, the rapid fluid compression and acceleration at the nose passing situation yields a pulse in the drag of the overtaken vehicle. The high pressure bow wave followed swiftly by the low-pressure wake affects the side force and lateral stability at positions slightly different than the nose passing.

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32

Evtikhov, Mikhail G., and Vladimir G. Evtikhov. "Computational experiment – nondimensionalization of equations, computational stability and program testing." Radioelectronics. Nanosystems. Information Technologies. 14, no. 3 (September 19, 2022): 331–40. http://dx.doi.org/10.17725/rensit.2022.14.331.

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From the stages of the computational experiment, the stage of non-dimensionalization of the initial equation (system of equations) of the problem is considered - the replacement of its variables by the product of the corresponding dimensionless quantities by their units of measurement with subsequent transformations. Such a transition from a physical model to a mathematical (dimensionless) one makes it possible to obtain software implementations for research. A critical evaluation of its complexity is carried out and possible errors in the results are evaluated. At the same time, new versions of software are formed. Object-oriented programming tools and version control systems (for example, git) allow you to create versions of software tools adapted to different conditions of their use and for different types of users. Parallelization of work on versions is carried out. At the same time, for further software implementation, the set-theoretic language of formulas with partially recursive functions is effective. To implement versions with large amounts of calculations and data, high-performance computing systems based on software and hardware acceleration, parallel information processing and cloud architectures are used. As a rule, a difference model of the problem and iterative methods for solving it are constructed for a program version. Computational stability conditions are usually stipulated in modern instructions for standard program libraries. For new algorithms, it is necessary to analyze the stability of difference schemes based on the refinement of their spectral properties and the use of functional analysis methods. For storage and subsequent application of the results of computational experiments, it is advisable to use modern databases. As a kind of computational experiment, testing of alpha and beta versions of programs and their releases is also considered.

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33

Xiao, S. P., and T. Belytschko. "Material stability analysis of particle methods." Advances in Computational Mathematics 23, no. 1-2 (July 2005): 171–90. http://dx.doi.org/10.1007/s10444-004-1817-5.

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34

Jahanshahloo, G. R., F. Hosseinzadeh, N. Shoja, M. Sanei, and G. Tohidi. "Sensitivity and stability analysis in DEA." Applied Mathematics and Computation 169, no. 2 (October 2005): 897–904. http://dx.doi.org/10.1016/j.amc.2004.09.092.

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35

Azhmyakov, Vadim. "Stability of differential inclusions: A computational approach." Mathematical Problems in Engineering 2006 (2006): 1–15. http://dx.doi.org/10.1155/mpe/2006/17837.

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We present a technique for analysis of asymptotic stability for a class of differential inclusions. This technique is based on the Lyapunov-type theorems. The construction of the Lyapunov functions for differential inclusions is reduced to an auxiliary problem of mathematical programming, namely, to the problem of searching saddle points of a suitable function. The computational approach to the auxiliary problem contains a gradient-type algorithm for saddle-point problems. We also extend our main results to systems described by difference inclusions. The obtained numerical schemes are applied to some illustrative examples.

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36

Sheina, E. A. "Numerical analysis of the stability of drift waves." Computational Mathematics and Modeling 3, no. 2 (1992): 252–55. http://dx.doi.org/10.1007/bf01127857.

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37

Hou, Thomas Y. "Blow-up or no blow-up? A unified computational and analytic approach to 3D incompressible Euler and Navier–Stokes equations." Acta Numerica 18 (May 2009): 277–346. http://dx.doi.org/10.1017/s0962492906420018.

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Whether the 3D incompressible Euler and Navier–Stokes equations can develop a finite-time singularity from smooth initial data with finite energy has been one of the most long-standing open questions. We review some recent theoretical and computational studies which show that there is a subtle dynamic depletion of nonlinear vortex stretching due to local geometric regularity of vortex filaments. We also investigate the dynamic stability of the 3D Navier–Stokes equations and the stabilizing effect of convection. A unique feature of our approach is the interplay between computation and analysis. Guided by our local non-blow-up theory, we have performed large-scale computations of the 3D Euler equations using a novel pseudo-spectral method on some of the most promising blow-up candidates. Our results show that there is tremendous dynamic depletion of vortex stretching. Moreover, we observe that the support of maximum vorticity becomes severely flattened as the maximum vorticity increases and the direction of the vortex filaments near the support of maximum vorticity is very regular. Our numerical observations in turn provide valuable insight, which leads to further theoretical breakthrough. Finally, we present a new class of solutions for the 3D Euler and Navier–Stokes equations, which exhibit very interesting dynamic growth properties. By exploiting the special nonlinear structure of the equations, we prove nonlinear stability and the global regularity of this class of solutions.

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38

Piqueras, M. A., R. Company, and L. Jódar. "Stable Numerical Solutions Preserving Qualitative Properties of Nonlocal Biological Dynamic Problems." Abstract and Applied Analysis 2019 (July 1, 2019): 1–7. http://dx.doi.org/10.1155/2019/5787329.

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This paper deals with solving numerically partial integrodifferential equations appearing in biological dynamics models when nonlocal interaction phenomenon is considered. An explicit finite difference scheme is proposed to get a numerical solution preserving qualitative properties of the solution. Gauss quadrature rules are used for the computation of the integral part of the equation taking advantage of its accuracy and low computational cost. Numerical analysis including consistency, stability, and positivity is included as well as numerical examples illustrating the efficiency of the proposed method.

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39

Melnik, R. V. N., and K. N. Zotsenko. "Mixed electroelastic waves and CFL stability conditions in computational piezoelectricity." Applied Numerical Mathematics 48, no. 1 (January 2004): 41–62. http://dx.doi.org/10.1016/j.apnum.2003.06.002.

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40

LUZYANINA, TATYANA, KOEN ENGELBORGHS, and DIRK ROOSE. "NUMERICAL BIFURCATION ANALYSIS OF DIFFERENTIAL EQUATIONS WITH STATE-DEPENDENT DELAY." International Journal of Bifurcation and Chaos 11, no. 03 (March 2001): 737–53. http://dx.doi.org/10.1142/s0218127401002407.

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In this paper we apply existing numerical methods for bifurcation analysis of delay differential equations with constant delay to equations with state-dependent delay. In particular, we study the computation, continuation and stability analysis of steady state solutions and periodic solutions. We collect the relevant theory and describe open theoretical problems in the context of bifurcation analysis. We present computational results for two examples and compare with analytical results whenever possible.

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41

Mastrogiuseppe, Francesca, and Srdjan Ostojic. "A Geometrical Analysis of Global Stability in Trained Feedback Networks." Neural Computation 31, no. 6 (June 2019): 1139–82. http://dx.doi.org/10.1162/neco_a_01187.

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Recurrent neural networks have been extensively studied in the context of neuroscience and machine learning due to their ability to implement complex computations. While substantial progress in designing effective learning algorithms has been achieved, a full understanding of trained recurrent networks is still lacking. Specifically, the mechanisms that allow computations to emerge from the underlying recurrent dynamics are largely unknown. Here we focus on a simple yet underexplored computational setup: a feedback architecture trained to associate a stationary output to a stationary input. As a starting point, we derive an approximate analytical description of global dynamics in trained networks, which assumes uncorrelated connectivity weights in the feedback and in the random bulk. The resulting mean-field theory suggests that the task admits several classes of solutions, which imply different stability properties. Different classes are characterized in terms of the geometrical arrangement of the readout with respect to the input vectors, defined in the high-dimensional space spanned by the network population. We find that such an approximate theoretical approach can be used to understand how standard training techniques implement the input-output task in finite-size feedback networks. In particular, our simplified description captures the local and the global stability properties of the target solution, and thus predicts training performance.

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Yin, Xiangjie, Hang Lin, Yifan Chen, Yixian Wang, and Yanlin Zhao. "Precise evaluation method for the stability analysis of multi-scale slopes." SIMULATION 96, no. 10 (August 3, 2020): 841–48. http://dx.doi.org/10.1177/0037549720943274.

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Slope stability analysis is a multi-scale problem. Typically, owing to the distinctions of slope scales (e.g., slope height or slope angle) in practical engineering, the stability calculation results of slopes with various scales from numerical methods inevitably exhibit different computational precision levels in the case of identical computational grids, and therefore the stability results of different slopes cannot be compared. To achieve equal accuracy stability analysis for multi-scale slopes, this study establishes numerical models of slopes with various scales as well as different grid shapes and sizes to conduct stability analysis. The results show the following: (a) a positive correlation relationship exists between the safety factor of the slope and the scaling factor, which is defined as the ratio of the grid size to the slope height; (b) the definition of the refined safety factor is given, representing the safety factor that corresponds to the infinitesimal grid size and eliminating the computational error of slope stability analysis caused by grid size or shape; (c) on this basis, embarking on the composite influence of multiple scales of slope on stability analysis, the study proposes a simplified treatment method suitable for evaluating the refined safety factor of the multi-scale slopes, which is verified as valid and feasible by some examples.

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Čiegis, R., and N. Tumanova. "Paralel Predictor-Corrector Schemes for Parabolic Problems on Graphs." Computational Methods in Applied Mathematics 10, no. 3 (2010): 275–82. http://dx.doi.org/10.2478/cmam-2010-0015.

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AbstractWe consider a predictor-corrector type finite difference scheme for solving one-dimensional parabolic problems. This algorithm decouples computations on different subdomains and thus can be efficiently implemented on parallel computers and used to solve problems on graph structures. The stability and convergence of the discrete solution is proved in the special energy and maximum norms. The results of computational experiments are presented.

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Niemiec, Dominik, Roman Bulko, and Juraj Mužík. "The Meshfree Localized Petrov-Galerkin Approach in Slope Stability Analysis." Civil and Environmental Engineering 15, no. 1 (June 1, 2019): 79–84. http://dx.doi.org/10.2478/cee-2019-0011.

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Abstract The article focuses on the use of the meshfree numerical method in the field of slope stability computations. There are many meshfree implementations of numerical methods. The article shows the results obtained using the meshfree localized Petrov-Galerkin method (MLPG) – localized weak-form of the equilibrium equations with an often used elastoplastic material model based on Mohr-Coulomb (MC) yield criterion. The most important aspect of MLPG is that the discretization process uses a set of nodes instead of elements. Node position within the computational domain is not restricted by any prescribed relationship. The shape functions are constructed using just the set of nodes present in the simple shaped domain of influence. The benchmark slope stability numerical model was performed using the developed meshfree computer code and compared with conventional finite element (FEM) and limit equilibrium (LEM) codes. The results showed the ability of the implemented theoretical preliminaries to solve the geotechnical stability problems.

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Mahdi, Mohammed, and Yasser A. Elhassan. "Stability Analysis of a Light Aircraft Configuration Using Computational Fluid Dynamics." Applied Mechanics and Materials 225 (November 2012): 391–96. http://dx.doi.org/10.4028/www.scientific.net/amm.225.391.

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This work aims to simulate and study the flow field around SAFAT-01 aircraft using numerical solution based on solving Reynolds Averaged Navier-Stokes equations coupled with K-ω SST turbulent model. The aerodynamics behavior of SAFAT-01 aircraft developed at SAFAT aviation complex were calculated at different angles of attack and side slip angles. The x,y and z forces and moments were calculated at flight speed 50m/s and at sea level condition. Lift and drag curves for different angles of attack were plotted. The maximum lift coefficient for SAFAT-01 was 1.67 which occurred at angle of attack 16° and Maximum lift to drag ratio (L/D) was 14 which occurred at α=3°, and the zero lift drag coefficient was 0.0342. Also the yawing moment coefficient was plotted for different side slip angles as well as rolling moment. The longitudinal stability derivatives with respect to angle of attack, speed variation (u), rate of pitch (q) and time rate of change of angle of attack were calculated using obtained CFD results. Concerning lateral stability only side slips derivatives were calculated. To validate this numerical simulation USAF Digital DATCOM is used to analyze this aircraft; a comparison between predicted results for this aircraft and Digital DATCOM indicated that this numerical simulation has high ability for predicting the aerodynamics characteristics.

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Sinha, S. C., Tai-Sheng Liu, and N. R. Senthilnathan. "A new computational technique for the stability analysis of slender rods." Archive of Applied Mechanics 62, no. 5 (May 1992): 347–60. http://dx.doi.org/10.1007/bf00788642.

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Arun, N. K., and B. M. Mohan. "Modeling, stability analysis and computational aspects of nonlinear fuzzy PID controllers." Journal of Intelligent & Fuzzy Systems 31, no. 3 (August 13, 2016): 1807–18. http://dx.doi.org/10.3233/jifs-152626.

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Bartels, Robert E. "Flexible Launch Stability Analysis Using Steady and Unsteady Computational Fluid Dynamics." Journal of Spacecraft and Rockets 49, no. 4 (July 2012): 644–50. http://dx.doi.org/10.2514/1.a32082.

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Sapagovas, Mifodijus, Regimantas Čiupaila, Živilė Jokšienė, and Tadas Meškauskas. "Computational Experiment for Stability Analysis of Difference Schemes with Nonlocal Conditions." Informatica 24, no. 2 (January 1, 2013): 275–90. http://dx.doi.org/10.15388/informatica.2013.396.

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Shimada, Toru, Masahisa Hanzawa, Takakazu Morita, Takashi Kato, Takashi Yoshikawa, and Yasuhiko Wada. "Stability Analysis of Solid Rocket Motor Combustion by Computational Fluid Dynamics." AIAA Journal 46, no. 4 (April 2008): 947–57. http://dx.doi.org/10.2514/1.31976.

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