Relevant bibliographies by topics / Pseudo-spectral based global collocation method

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers

Academic literature on the topic 'Pseudo-spectral based global collocation method'

Author: Grafiati
Published: 6 September 2023
Last updated: 31 July 2025

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Journal articles on the topic "Pseudo-spectral based global collocation method"

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Izadi, Mohammad, and Hari Mohan Srivastava. "Applications of Modified Bessel Polynomials to Solve a Nonlinear Chaotic Fractional-Order System in the Financial Market: Domain-Splitting Collocation Techniques." Computation 11, no. 7 (2023): 130. http://dx.doi.org/10.3390/computation11070130.

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We propose two accurate and efficient spectral collocation techniques based on a (novel) domain-splitting strategy to handle a nonlinear fractional system consisting of three ODEs arising in financial modeling and with chaotic behavior. One of the major numerical difficulties in designing traditional spectral methods is in the handling of model problems on a long computational domain, which usually yields to loss of accuracy. One remedy is to split the underlying domain and apply the spectral method locally in each subdomain rather than on the global domain of interest. To treat the chaotic fi
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Khanduzi, Raheleh, Asyieh Ebrahimzadeh, and Samaneh Panjeh Ali Beik. "Optimal control of fractional integro-differential systems based on a spectral method and grey wolf optimizer." An International Journal of Optimization and Control: Theories & Applications (IJOCTA) 10, no. 1 (2020): 55–65. http://dx.doi.org/10.11121/ijocta.01.2020.00753.

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This paper elaborated an effective and robust metaheuristic algorithm with acceptable performance based on solution accuracy. The algorithm applied in solution of the optimal control of fractional Volterra integro-differential (FVID) equation which be substituted by nonlinear programming (NLP). Subsequently the FIVD convert the problem to a NLP by using spectral collocation techniques and thereafter we execute the grey wolf optimizer (GWO) to improve the speed and accuracy and find the solutions of the optimal control and state as well as the optimal value of the cost function. It is mentioned
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Khader, M. M., and Mohammed M. Babatin. "On Approximate Solutions for Fractional Logistic Differential Equation." Mathematical Problems in Engineering 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/391901.

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A new approximate formula of the fractional derivatives is derived. The proposed formula is based on the generalized Laguerre polynomials. Global approximations to functions defined on a semi-infinite interval are constructed. The fractional derivatives are presented in terms of Caputo sense. Special attention is given to study the convergence analysis and estimate an error upper bound of the presented formula. The new spectral Laguerre collocation method is presented for solving fractional Logistic differential equation (FLDE). The properties of Laguerre polynomials approximation are used to
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Ibrahim, Yasser F., Sobhi E. Abd El-Bar, Mohamed M. Khader, and Mohamed Adel. "Studying and Simulating the Fractional COVID-19 Model Using an Efficient Spectral Collocation Approach." Fractal and Fractional 7, no. 4 (2023): 307. http://dx.doi.org/10.3390/fractalfract7040307.

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We give a theoretical and numerical analysis of a coronavirus (COVID-19) infection model in this research. A mathematical model of this system is provided, based on a collection of fractional differential equations (in the Caputo sense). Initially, a rough approximation formula was created for the fractional derivative of tp. Here, the third-kind Chebyshev approximations of the spectral collocation method (SCM) were used. To identify the unknown coefficients of the approximate solution, the proposed problem was transformed into a system of algebraic equations, which was then transformed into a
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CHAKRABORTY, DEBANANDA, JAE-HUN JUNG, and GAURAV KHANNA. "A MULTI-DOMAIN HYBRID METHOD FOR HEAD-ON COLLISION OF BLACK HOLES IN PARTICLE LIMIT." International Journal of Modern Physics C 22, no. 05 (2011): 517–41. http://dx.doi.org/10.1142/s0129183111016415.

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A hybrid method is developed based on the spectral and finite-difference methods for solving the inhomogeneous Zerilli equation in time-domain. The developed hybrid method decomposes the domain into the spectral and finite-difference domains. The singular source term is located in the spectral domain while the solution in the region without the singular term is approximated by the higher-order finite-difference method. The spectral domain is also split into multi-domains and the finite-difference domain is placed as the boundary domain. Due to the global nature of the spectral method, a multi-
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Sánchez, José L. Carrión, Sílvio R. C. de Freitas, and Riccardo Barzaghi. "OFFSET EVALUATION OF THE ECUADORIAN VERTICAL DATUM RELATED TO THE IHRS." Boletim de Ciências Geodésicas 24, no. 4 (2018): 503–25. http://dx.doi.org/10.1590/s1982-21702018000400031.

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Abstract Considering the definition of the International Height Reference System (IHRS) in the geopotential space (Resolution 1/2015, International Association of Geodesy - IAG), among the present main objectives of the international geodetic community is the materialization of IHRS around the world. One fundamental task for this is the offset determination of each national vertical datum related to the IHRS. In this manuscript we establish the relationship between the Ecuadorian Vertical Datum (EVD) and the IHRS in the geopotential space following the foundations of the Resolution 1/2015 IAG.
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Zhang, Jing, Xiaokai Zhu, Te Chen, and Guowei Dou. "Optimal Dynamics Control in Trajectory Tracking of Industrial Robots Based on Adaptive Gaussian Pseudo-Spectral Algorithm." Algorithms 18, no. 1 (2025): 18. https://doi.org/10.3390/a18010018.

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A pseudo-spectral control algorithm based on adaptive Gauss collocation point reconstruction is proposed to efficiently solve the optimal dynamics control problem of industrial robots. A mathematical model for the kinematic relationship and dynamic optimization control of industrial robots has been established. On the basis of deriving the Legendre–Gauss collocation formula, a two-stage adaptive Gauss collocation strategy for industrial robot dynamics control variables was designed to improve the dynamics optimization control effect of industrial robot by improving the solution efficiency of c
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Kim, Chang Ho, and U. Jin Choi. "Spectral collocation methods for a partial integro-differential equation with a weakly singular kernel." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 39, no. 3 (1998): 408–30. http://dx.doi.org/10.1017/s0334270000009474.

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AbstractWe propose and analyze the spectral collocation approximation for the partial integro-differential equations with a weakly singular kernel. The space discretization is based on the pseudo-spectral method, which is a collocation method at the Gauss-Lobatto quadrature points. We prove unconditional stability and obtain the optimal error bounds which depend on the time step, the degree of polynomial and the Sobolev regularity of the solution.
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Vergos, Georgios S., Ilias N. Tziavos, Stelios Mertikas, Dimitrios Piretzidis, Xenofon Frantzis, and Craig Donlon. "Local Gravity and Geoid Improvements around the Gavdos Satellite Altimetry Cal/Val Site." Remote Sensing 16, no. 17 (2024): 3243. http://dx.doi.org/10.3390/rs16173243.

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The isle of Gavdos, and its wider area, is one of the few places worldwide where the calibration and validation of altimetric satellites has been carried out during the last, more than, two decades using dedicated techniques at sea and on land. The sea-surface calibration employed for the determination of the bias in the satellite altimeter’s sea-surface height relies on the use of a gravimetric geoid in collocation with data from tide gauges, permanent global navigation satellite system (GNSS) receivers, as well as meteorological and oceanographic sensors. Hence, a high-accuracy and high-reso
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Bhrawy, A. H., M. A. Alghamdi, and D. Baleanu. "Numerical Solution of a Class of Functional-Differential Equations Using Jacobi Pseudospectral Method." Abstract and Applied Analysis 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/513808.

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The shifted Jacobi-Gauss-Lobatto pseudospectral (SJGLP) method is applied to neutral functional-differential equations (NFDEs) with proportional delays. The proposed approximation is based on shifted Jacobi collocation approximation with the nodes of Gauss-Lobatto quadrature. The shifted Legendre-Gauss-Lobatto Pseudo-spectral and Chebyshev-Gauss-Lobatto Pseudo-spectral methods can be obtained as special cases of the underlying method. Moreover, the SJGLP method is extended to numerically approximate the nonlinear high-order NFDE with proportional delay. Some examples are displayed for implicit
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Dissertations / Theses on the topic "Pseudo-spectral based global collocation method"

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Swaminathan, Shriram. "Real Time Solutions to Aerospace Optimal Control Problems." Thesis, 2020. https://etd.iisc.ac.in/handle/2005/5082.

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A real-time autonomous trajectory generation methodology for aerospace vehicles using pseudo-spectral based global collocation methods is presented in this thesis. The proposed method is formulated in a manner whereby it can converge from random initial guess pro les in real time. The proposed methodology is validated using Monte-Carlo simulations for various practical aerospace problems to demonstrate the robustness in presence of initial condition errors. In the thesis, the solution to the trajectory optimization using both Direct and In- direct methods are presented. A two level opti
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Book chapters on the topic "Pseudo-spectral based global collocation method"

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Natsiopoulos, D. A., E. G. Mamagiannou, A. Triantafyllou, et al. "Newly Acquired Gravity Data in Support of the GeoNetGNSS CORS Network in Northern Greece." In International Association of Geodesy Symposia. Springer Berlin Heidelberg, 2023. http://dx.doi.org/10.1007/1345_2023_213.

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AbstractThe main purpose of the GeoNetGNSS project, funded by the European Union and National Funds through the Region of Central Macedonia (RCM), is to establish a dense network of Continuously Operating Reference Stations (CORS) in northern Greece to support geodetic, surveying, engineering, and mapping applications. A regional, high-accuracy and high-resolution gravimetric geoid model is essential for the accurate determination of physical heights from CORS so as to transform the geometric heights into orthometric ones. In that frame and given the geological complexity and topographic pecul
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Conference papers on the topic "Pseudo-spectral based global collocation method"

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Zhang, Ce, Wei Ma, Wensheng Yu, and Jinfang Teng. "Effect of Heat Transfer on Pipe Flow Stability." In ASME Turbo Expo 2017: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/gt2017-64451.

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The compressibility of flow field has an important effect on flow stability. However, when the compressibility is considered, the effect of Mach number is often considered while the effect of heat transfer is always neglected in the existing flow stability studies. Linear stability analysis tools based on compressible Orr-Sommerfeld (O-S) equations and linearized Navier-Stokes equations in cylindrical coordinate system are established in this paper. These equations are numerically solved by using Chebyshev spectral collocation method and pseudo-modes are eliminated. Linear stability analysis o
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Chen, He, Sun Dakun, and Sun Xiaofeng. "Stall Inception Analysis of Transonic Compressors With Chordwise and Axial Sweep." In ASME Turbo Expo 2017: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/gt2017-63174.

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This paper concentrates on the stall inception analysis of transonic compressors with chordwise and axial sweep. A new prediction approach of stall inception is developed based on global stability analysis and immersed boundary theory, which makes it possible to takes both the concrete blade geometry and complicated base flow into consideration. The prediction of stall inception boils down to an eigenvalue problem. Spectral collocation method is adopted to discretize the eigenvalue equations and the eigenvalues are solved by using singular value decomposition method. The developed prediction a
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Kaloni, P. N., and J. X. Lou. "Convective Stability of Hadley Circulations in Finite Domains." In ASME 2010 3rd Joint US-European Fluids Engineering Summer Meeting collocated with 8th International Conference on Nanochannels, Microchannels, and Minichannels. ASMEDC, 2010. http://dx.doi.org/10.1115/fedsm-icnmm2010-31228.

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We present numerical solutions of natural convection in a cavity of finite domain when the flow is driven by a horizontal temperature gradient between isothermal vertical walls. Only the transverse roll structure of convection is calculated by employing the pseudo spectral Chebyshev collocation method. A numerical solution of the steady flow is first obtained and, based upon it, the critical Rayleigh number (related to Grashof number) of linear transverse mode is determined. The influence of aspect ratio, on the flow and temperature patterns, is also investigated.
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Iklódi, Zsolt, Xavier Beudaert, and Zoltan Dombovari. "On the Modelling Bases of In-Motion Dynamic Characterization of Flexible Structures Subject to Friction and Position Control Delay." In ASME 2022 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2022. http://dx.doi.org/10.1115/detc2022-90924.

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Abstract This article presents a characterisation technique of in-motion machine dynamics based on the principles of numerical continuation. A linear two degree of freedom mechanical model is considered, representing e.g. a flexible moving column of a machine tool, and is subjected to a non-smooth friction and a delayed feedback drive control force, resulting in a model governed by a system of piecewise-smooth delay differential equations. By applying harmonic forcing to the system, periodic solutions can be found, through the continuation of which, an accurate vibratory characterisation of in
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Lee, Hyungtae, Joongyu Kim, Jongoh Kim, et al. "An Efficient Time Domain Structural Assessment of a Floating Wind Turbine Structure." In ASME 2023 42nd International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2023. http://dx.doi.org/10.1115/omae2023-108155.

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Abstract Unlike conventional offshore production platform, a substructure supporting floating offshore wind turbine has unique structural characteristics due to higher frequency aeroelastic loading from wind turbine in addition to wave loading. Due to periodic rotation of turbine, a floating offshore turbine substructure experiences higher fatigue load than conventional offshore platform. A reliable fatigue assessment is required to achieve the structural safety and integrity of the floating wind turbine platform. Accordingly, class societies recommend fully coupled time domain analysis becaus
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Babaee, Hessam, Sumanta Acharya, and Xiaoliang Wan. "Optimization of Forcing Parameters of Film Cooling Effectiveness." In ASME Turbo Expo 2013: Turbine Technical Conference and Exposition. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/gt2013-95636.

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An optimization strategy is described that combines high-fidelity simulations with response surface construction, and is applied to pulsed film cooling for turbine blades. The response surface is constructed for the film cooling effectiveness as a function of duty cycle, in the range of DC between 0.05 and 1, and pulsation frequency St in the range of 0.2–2, using a pseudo-spectral projection method. The jet is fully modulated and the blowing ratio, when the jet is on, is 1.5 in all cases. Overall 73 direct numerical simulations (DNS) using spectral element method were performed to sample the
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