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Journal articles on the topic 'Numerical solutions'

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Author: Grafiati

Published: 4 June 2021

Last updated: 30 July 2024

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1

ROTARU, Constantin. "NUMERICAL SOLUTIONS FOR COMBUSTION WAVE VELOCITY." SCIENTIFIC RESEARCH AND EDUCATION IN THE AIR FORCE 21, no. 1 (October 8, 2019): 184–93. http://dx.doi.org/10.19062/2247-3173.2019.21.25.

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2

Attwood, G. B., and David Tall. "Numerical Solutions of Equations." Mathematical Gazette 78, no. 481 (March 1994): 77. http://dx.doi.org/10.2307/3619449.

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3

Xinfu, Chen, Charlie M. Elliot, Gardiner Andy, and Jennifer Jing Zhao. "Convergence of numerical solutions." Applicable Analysis 69, no. 1-2 (June 1998): 95–108. http://dx.doi.org/10.1080/00036819808840645.

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4

Demidov, A. S. "Inverse, ill-posed problems, essentially different solutions and explicit formulas for solutions." Journal of Physics: Conference Series 2092, no. 1 (December 1, 2021): 012016. http://dx.doi.org/10.1088/1742-6596/2092/1/012016.

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Abstract A request for an inverse problem, as well as for an incorrect problem produces tens of millions of answers in the Internet. In the past few decades, hundreds of international conferences on these topics have been held annually. Problems of this kind are quite involved, and their numerical analysis requires the development of special methods and numerical algorithms. Explicit formulas provide the main tool for testing these methods and numerical algorithms. The Cauchy problem for an elliptic equation is a classical ill-posed problem, which serves as a model for many inverse and incorrect problems. In the present paper we give a numerically realizable explicit formula for solving the Cauchy problem in a two-dimensional domain for a general second-order linear elliptic equation with analytic coefficients and the Cauchy analytic data on the analytic boundary.

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5

Wu, G., Eric Wai Ming Lee, and Gao Li. "Numerical solutions of the reaction-diffusion equation." International Journal of Numerical Methods for Heat & Fluid Flow 25, no. 2 (March 2, 2015): 265–71. http://dx.doi.org/10.1108/hff-04-2014-0113.

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Purpose – The purpose of this paper is to introduce variational iteration method (VIM) to construct equivalent integral equations for initial-boundary value problems of nonlinear partial differential equations. The Lagrange multipliers become the integral kernels. Design/methodology/approach – Using the discrete numerical integral formula, the general way is given to solve the famous reaction-diffusion equation numerically. Findings – With the given explicit solution, the results show the conveniences of the general numerical schemes and numerical simulation of the reaction-diffusion is finally presented in the cases of various coefficients. Originality/value – The method avoids the treatment of the time derivative as that in the classical finite difference method and the VIM is introduced to construct equivalent integral equations for initial-boundary value problems of nonlinear partial differential equations.

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6

Isakari, Shirley M., and Richard C. J. Somerville. "Accurate numerical solutions for Daisyworld." Tellus B: Chemical and Physical Meteorology 41, no. 4 (July 1989): 478–82. http://dx.doi.org/10.3402/tellusb.v41i4.15103.

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7

ISAKARI, SHIRLEY M., and RICHARD C. J. SOMERVILLE. "Accurate numerical solutions for Daisyworld." Tellus B 41B, no. 4 (September 1989): 478–82. http://dx.doi.org/10.1111/j.1600-0889.1989.tb00324.x.

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8

Rioux, Frank. "Numerical solutions for Schroedinger's equation." Journal of Chemical Education 67, no. 9 (September 1990): 770. http://dx.doi.org/10.1021/ed067p770.1.

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9

Laponin, V. S., N. P. Savenkova, and V. P. Il’yutko. "Numerical method for soliton solutions." Computational Mathematics and Modeling 23, no. 3 (July 2012): 254–65. http://dx.doi.org/10.1007/s10598-012-9135-0.

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10

Galiyev, Sh I. "Numerical solutions of minmaxmin problems." USSR Computational Mathematics and Mathematical Physics 28, no. 4 (January 1988): 25–32. http://dx.doi.org/10.1016/0041-5553(88)90107-3.

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11

Remillard, Wilfred J. "Numerical solutions of Poisson's formula." Journal of the Acoustical Society of America 89, no. 2 (February 1991): 939–42. http://dx.doi.org/10.1121/1.1894656.

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12

Galybin, A. N. "Numerical solutions for polygonal cracks." International Journal of Fracture 131, no. 2 (January 2005): L15—L20. http://dx.doi.org/10.1007/s10704-005-2595-x.

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13

Du, Ying, and Changlin Mei. "A Compensated Numerical Method for Solving Stochastic Differential Equations with Variable Delays and Random Jump Magnitudes." Mathematical Problems in Engineering 2015 (2015): 1–11. http://dx.doi.org/10.1155/2015/810160.

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Stochastic differential equations with jumps are of a wide application area especially in mathematical finance. In general, it is hard to obtain their analytical solutions and the construction of some numerical solutions with good performance is therefore an important task in practice. In this study, a compensated split-stepθmethod is proposed to numerically solve the stochastic differential equations with variable delays and random jump magnitudes. It is proved that the numerical solutions converge to the analytical solutions in mean-square with the approximate rate of 1/2. Furthermore, the mean-square stability of the exact solutions and the numerical solutions are investigated via a linear test equation and the results show that the proposed numerical method shares both the mean-square stability and the so-called A-stability.

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14

Ziener, C. H., T. Kampf, H.-P. Schlemmer, and L. R. Buschle. "Spin echoes: full numerical solution and breakdown of approximative solutions." Journal of Physics: Condensed Matter 31, no. 15 (February 21, 2019): 155101. http://dx.doi.org/10.1088/1361-648x/aafe21.

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15

Bueler, Ed, Craig S. Lingle, Jed A. Kallen-Brown, David N. Covey, and Latrice N. Bowman. "Exact solutions and verification of numerical models for isothermal ice sheets." Journal of Glaciology 51, no. 173 (2005): 291–306. http://dx.doi.org/10.3189/172756505781829449.

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AbstractComparison of numerically computed solutions to exact (analytical) time-dependent solutions, when possible, is superior to intercomparison as a technique for verification of numerical models. At least two sources of such exact solutions exist for the isothermal shallow ice-sheet equation: similarity solutions and solutions with ‘compensatory accumulation’. In this paper, we derive new similarity solutions with non-zero accumulation. We also derive exact solutions with (i) sinusoidal-in-time accumulation and (ii) basal sliding. A specific test suite based on these solutions is proposed and used to verify a standard explicit finite-difference method. This numerical scheme is shown to reliably track the position of a moving margin while being characterized by relatively large thickness errors near the margin. The difficulty of approximating the margin essentially explains the rate of global convergence of the numerical method. A transformed version of the ice-sheet equation eliminates the singularity of the margin shape and greatly accelerates the convergence. We also use an exact solution to verify an often-used numerical approximation for basal sliding and we discuss improvements of existing benchmarks.

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16

ÜNAL, Osman, and Nuri AKKAŞ. "Tandem Kaynak İşleminde Sıcaklık Dağılımının Sayısal Analizi." Karadeniz Fen Bilimleri Dergisi 12, no. 1 (June 15, 2022): 1–21. http://dx.doi.org/10.31466/kfbd.996230.

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In this study, the numerical solutions for the steady-state heat conduction problem with uniform heat source, the steady-state heat conduction problem with convective heat transfer and the transient heat conduction problem have been developed using finite difference method. These numerical solutions have been validated with analytical solutions. After observing the good agreements between numerical solutions and analytical solutions, these three different problems combined to simulate the tandem welding process. The first objective of this study is to present a numerical simulator for the transient heat conduction problem that includes non-uniform moving heat sources and convective heat transfer term. This numerical simulator contains explicit and implicit time discretization methods. In this simulator, it is possible to change the grid sizes, time step sizes, total simulation time, distance between electrodes, magnitude of the sources' power, speed of the sources, etc. Secondly, the temperature distribution of single and twin wire welding processes have been compared using proposed numerical simulator to investigate the premature solidification of liquid metal in low-temperature zone of molten pool. Thirdly, experimental study was carried out using Fluke Thermal Imager to validate numerical results. It was obtained that the maximum temperature of numerical result is very close to the maximum temperature of experimental result with 0.248 % error. Finally, the all Matlab codes related to developed numerical simulator have been added to Appendix to facilitate other researchers’ work.

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17

Khuri, Suheil A., and Ali M. Sayfy. "NUMERICAL SOLUTION OF A CLASS OF NONLINEAR SYSTEM OF SECOND-ORDER BOUNDARY-VALUE PROBLEMS: A FOURTH-ORDER CUBIC SPLINE APPROACH." Mathematical Modelling and Analysis 20, no. 5 (September 28, 2015): 681–700. http://dx.doi.org/10.3846/13926292.2015.1091793.

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A cubic B-spline collocation approach is described and presented for the numerical solution of an extended system of linear and nonlinear second-order boundary-value problems. The system, whether regular or singularly perturbed, is tackled using a spline collocation approach constructed over uniform or non-uniform meshes. The rate of convergence is discussed theoretically and verified numerically to be of fourth-order. The efficiency and applicability of the technique are demonstrated by applying the scheme to a number of linear and nonlinear examples. The numerical solutions are contrasted with both analytical and other existing numerical solutions that exist in the literature. The numerical results demonstrate that this method is superior as it yields more accurate solutions.

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18

Bekir, A., M. Shehata, and E. Zahran. "Comparison Between the Exact Solutions of Three Distinct Shallow Water Equations Using the Painlevé Approach and Its Numerical Solutions." Nelineinaya Dinamika 16, no. 3 (2020): 463–77. http://dx.doi.org/10.20537/nd200305.

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19

Ahmad, Khan, and Cesarano. "Numerical Solutions of Coupled Burgers′ Equations." Axioms 8, no. 4 (October 23, 2019): 119. http://dx.doi.org/10.3390/axioms8040119.

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In this article, two new modified variational iteration algorithms are investigated for the numerical solution of coupled Burgers′ equations. These modifications are made with the help of auxiliary parameters to speed up the convergence rate of the series solutions. Three numerical test problems are given to judge the behavior of the modified algorithms, and error norms are used to evaluate the accuracy of the method. Numerical simulations are carried out for different values of parameters. The results are also compared with the existing methods in the literature.

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20

Kouri, D. J., D. S. Zhang, G. W. Wei, T. Konshak, and D. K. Hoffman. "Numerical solutions of nonlinear wave equations." Physical Review E 59, no. 1 (January 1, 1999): 1274–77. http://dx.doi.org/10.1103/physreve.59.1274.

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21

Schetz, J. A., F. S. Billig, and S. Favin. "Numerical solutions of scramjet nozzle flows." Journal of Propulsion and Power 3, no. 5 (September 1987): 440–47. http://dx.doi.org/10.2514/3.23008.

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22

Mitchell, G. P., and D. R. J. Owen. "Numerical solutions for elastic‐plastic problems." Engineering Computations 5, no. 4 (April 1988): 274–84. http://dx.doi.org/10.1108/eb023746.

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23

Karabenli, Hatice. "Numerical solutions for a Stefan problem." New Trends in Mathematical Science 4, no. 4 (October 30, 2016): 175. http://dx.doi.org/10.20852/ntmsci.2016422668.

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24

CAHLON, B., and D. SCHMIDT. "Numerical solutions for functional integral equations." IMA Journal of Numerical Analysis 12, no. 4 (1992): 527–43. http://dx.doi.org/10.1093/imanum/12.4.527.

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25

Matsuura, T., S. Saitoh †, and D. D. Trong ‡. "Numerical solutions of the poisson equation." Applicable Analysis 83, no. 10 (October 2004): 1037–51. http://dx.doi.org/10.1080/00036810410001724616.

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26

Zhou, S., and D. R. Westbrook. "Numerical solutions of the thermistor equations." Journal of Computational and Applied Mathematics 79, no. 1 (March 1997): 101–18. http://dx.doi.org/10.1016/s0377-0427(96)00166-5.

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27

Gash, Philip W. "Improved numerical solutions of Laplace’s equation." American Journal of Physics 59, no. 6 (June 1991): 509–15. http://dx.doi.org/10.1119/1.16810.

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28

Senn, Peter. "Numerical solutions of the Schrödinger equation." American Journal of Physics 60, no. 9 (September 1992): 776. http://dx.doi.org/10.1119/1.17093.

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29

Riveros, Oscar J. "Numerical solutions for liquid-junction potentials." Journal of Physical Chemistry 96, no. 14 (July 1992): 6001–4. http://dx.doi.org/10.1021/j100193a065.

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30

Liu, Shijie. "Transport Phenomena: Equations and Numerical Solutions." Chemical Engineering Journal 84, no. 3 (December 2001): 605–6. http://dx.doi.org/10.1016/s1385-8947(00)00387-9.

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31

Hou, Thomas Y. "Numerical Solutions to Free Boundary Problems." Acta Numerica 4 (January 1995): 335–415. http://dx.doi.org/10.1017/s0962492900002567.

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Many physically interesting problems involve propagation of free surfaces. Vortex-sheet roll-up in hydrodynamic instability, wave interactions on the ocean's free surface, the solidification problem for crystal growth and Hele-Shaw cells for pattern formation are some of the significant examples. These problems present a great challenge to physicists and applied mathematicians because the underlying problem is very singular. The physical solution is sensitive to small perturbations. Naïve discretisations may lead to numerical instabilities. Other numerical difficulties include singularity formation and possible change of topology in the moving free surfaces, and the severe time-stepping stability constraint due to the stiffness of high-order regularisation effects, such as surface tension.This paper reviews some of the recent advances in developing stable and efficient numerical algorithms for solving free boundary-value problems arising from fluid dynamics and materials science. In particular, we will consider boundary integral methods and the level-set approach for water waves, general multi-fluid interfaces, Hele–Shaw cells, crystal growth and solidification. We will also consider the stabilising effect of surface tension and curvature regularisation. The issue of numerical stability and convergence will be discussed, and the related theoretical results for the continuum equations will be addressed. This paper is not intended to be a detailed survey and the discussion is limited by both the taste and expertise of the author.

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32

Ma, Ming, Menahem Friedman, and Abraham Kandel. "Numerical solutions of fuzzy differential equations." Fuzzy Sets and Systems 105, no. 1 (July 1999): 133–38. http://dx.doi.org/10.1016/s0165-0114(97)00233-9.

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33

Afrouzi, G. A., and S. Khademloo. "Numerical solutions of diffusive logistic equation." Chaos, Solitons & Fractals 31, no. 1 (January 2007): 112–18. http://dx.doi.org/10.1016/j.chaos.2005.09.034.

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34

Kawala, A. M. "Numerical Solutions for Ito Coupled System." Acta Applicandae Mathematicae 106, no. 3 (October 10, 2008): 325–35. http://dx.doi.org/10.1007/s10440-008-9300-9.

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35

Saatdjian,, E., and WS Janna,. "Transport Phenomena: Equations and Numerical Solutions." Applied Mechanics Reviews 54, no. 4 (July 1, 2001): B72—B73. http://dx.doi.org/10.1115/1.1383685.

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36

Qi, Wang. "Numerical Solutions of Fractional Boussinesq Equation." Communications in Theoretical Physics 47, no. 3 (March 2007): 413–20. http://dx.doi.org/10.1088/0253-6102/47/3/007.

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37

Williams, A. G., L. R. Dodd, and A. W. Thomas. "The colour-dielectric model: Numerical solutions." Physics Letters B 176, no. 1-2 (August 1986): 158–62. http://dx.doi.org/10.1016/0370-2693(86)90943-3.

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38

Vahidi, A. R., E. Babolian, and Gh Asadi Cordshooli. "Numerical solutions of Duffing’s oscillator problem." Indian Journal of Physics 86, no. 4 (April 2012): 311–15. http://dx.doi.org/10.1007/s12648-012-0068-4.

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39

Molabahrami, A., and F. Khani. "Numerical solutions of highly oscillatory integrals." Applied Mathematics and Computation 198, no. 2 (May 2008): 657–64. http://dx.doi.org/10.1016/j.amc.2007.09.007.

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40

Rashed, M. T. "Numerical solutions of functional integral equations." Applied Mathematics and Computation 156, no. 2 (September 2004): 507–12. http://dx.doi.org/10.1016/j.amc.2003.08.003.

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41

Al-Khaled, Kamel. "Numerical solutions of the Laplace’s equation." Applied Mathematics and Computation 170, no. 2 (November 2005): 1271–83. http://dx.doi.org/10.1016/j.amc.2005.01.018.

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42

RAUF, ABDUL, TAHIR MUSHTAQ QURESHI, and CONSTANTIN FETECAU. "ANALYTICAL AND NUMERICAL SOLUTIONS FOR SOME." Mathematical Reports 25(75), no. 3 (2023): 465–79. http://dx.doi.org/10.59277/mrar.2023.25.75.3.465.

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Oscillatory motions of incompressible viscous fluids with exponential dependence of viscosity on the pressure between infinite horizontal parallel plates are analytically and numerically studied. The fluid motion is generated by the lower plate that oscillates in its plane and exact expressions are established for the steady-state solutions. The convergence of starting solutions to the corresponding steady-state solutions is graphically proved. The steady solutions corresponding to the simple Couette flow of the same fluids are obtained as limiting cases of the previous solutions. As expected, the fluid velocity diminishes for increasing values of the pressure-viscosity coefficient and ordinary fluids flow faster. The time required to reach the steady-state is graphically approximated. The spatial profiles of the starting solutions are presented both for oscillatory motions and the simple Couette flow.

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43

Cazacu, Nina N. "Numerical solutions of the differential equations." Annals of the ”Dunarea de Jos” University of Galati Fascicle II Mathematics Physics Theoretical Mechanics 46, no. 1 (September 11, 2023): 39–44. http://dx.doi.org/10.35219/ann-ugal-math-phys-mec.2023.1.07.

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In this paper, we propose to study the numerical integration of Cauchy's problem (PC-in short) for a system of differential equations of the first order by the method of successive approximations and the method of the polygonal line, the best known in practice. For example, the methods are applied to some particular functions. The novelty of this paper consists, mainly, in the translation of existing approximation methods into C++ code, in order to visualize the results including the graphic image of both approximate and exact values trajectories, for comparison.

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44

Zhang, Xiangzhi, and Yufeng Zhang. "Some Similarity Solutions and Numerical Solutions to the Time-Fractional Burgers System." Symmetry 11, no. 1 (January 18, 2019): 112. http://dx.doi.org/10.3390/sym11010112.

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In the paper, we discuss some similarity solutions of the time-fractional Burgers system (TFBS). Firstly, with the help of the Lie-point symmetry and the corresponding invariant variables, we transform the TFBS to a fractional ordinary differential system (FODS) under the case where the time-fractional derivative is the Riemann–Liouville type. The FODS can be approximated by some integer-order ordinary differential equations; here, we present three such integer-order ordinary differential equations (called IODE-1, IODE-2, and IODE-3, respectively). For IODE-1, we obtain its similarity solutions and numerical solutions, which approximate the similarity solutions and the numerical solutions of the TFBS. Secondly, we apply the numerical analysis method to obtain the numerical solutions of IODE-2 and IODE-3.

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45

Ravshanov, Normaxmad, and Bozorboy Yusupovich Palvanov. "NUMERICAL SOLUTION OF INVERSE PROBLEMS FILTERING PROCESS OF LOW-CONCENTRATION SOLUTIONS." Theoretical & Applied Science 48, no. 04 (April 30, 2017): 137–44. http://dx.doi.org/10.15863/tas.2017.04.48.22.

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46

Cahlon, Baruch, and Louis J. Nachman. "Numerical solutions of Volterra integral equations with a solution dependent delay." Journal of Mathematical Analysis and Applications 112, no. 2 (December 1985): 541–62. http://dx.doi.org/10.1016/0022-247x(85)90262-8.

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47

Ma, Shichang, Yufeng Xu, and Wei Yue. "Numerical Solutions of a Variable-Order Fractional Financial System." Journal of Applied Mathematics 2012 (2012): 1–14. http://dx.doi.org/10.1155/2012/417942.

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The numerical solution of a variable-order fractional financial system is calculated by using the Adams-Bashforth-Moulton method. The derivative is defined in the Caputo variable-order fractional sense. Numerical examples show that the Adams-Bashforth-Moulton method can be applied to solve such variable-order fractional differential equations simply and effectively. The convergent order of the method is also estimated numerically. Moreover, the stable equilibrium point, quasiperiodic trajectory, and chaotic attractor are found in the variable-order fractional financial system with proper order functions.

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48

Ali, Khalid K., and M. S. Mehanna. "Traveling wave solutions and numerical solutions of Gilson–Pickering equation." Results in Physics 28 (September 2021): 104596. http://dx.doi.org/10.1016/j.rinp.2021.104596.

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49

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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50

Yokuş, Asıf, and Doğan Kaya. "Comparison exact and numerical simulation of the traveling wave solution in nonlinear dynamics." International Journal of Modern Physics B 34, no. 29 (October 21, 2020): 2050282. http://dx.doi.org/10.1142/s0217979220502823.

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The traveling wave solutions of the combined Korteweg de Vries-modified Korteweg de Vries (cKdV-mKdV) equation and a complexly coupled KdV (CcKdV) equation are obtained by using the auto-Bäcklund Transformation Method (aBTM). To numerically approximate the exact solutions, the Finite Difference Method (FDM) is used. In addition, these exact traveling wave solutions and numerical solutions are compared by illustrating the tables and figures. Via the Fourier–von Neumann stability analysis, the stability of the FDM with the cKdV–mKdV equation is analyzed. The [Formula: see text] and [Formula: see text] norm errors are given for the numerical solutions. The 2D and 3D figures of the obtained solutions to these equations are plotted.

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