Numerical solution for a class of parabolic integro-differential equations subject to integral boundary conditions

Many physical phenomena can be modelled through nonlocal boundary value problems whose boundary conditions involve integral terms. In this work we propose a numerical algorithm, by combining second-order Crank–Nicolson schema for the temporal discretization and Legendre–Chebyshev pseudo-spectral met...

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Bibliographic Details
Published inArabian Journal of Mathematics Vol. 11; no. 2; pp. 213 - 225
Main Author Chattouh, Abdeldjalil
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2022
Springer
Springer Nature B.V
Subjects
Accuracy
Algorithms
Boundary conditions
Boundary value problems
Chebyshev approximation
Differential equations
Discretization
Mathematics
Mathematics and Statistics
Methods
Numerical analysis
Polynomials
Spectral methods
35R09
65M20
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Summary:Many physical phenomena can be modelled through nonlocal boundary value problems whose boundary conditions involve integral terms. In this work we propose a numerical algorithm, by combining second-order Crank–Nicolson schema for the temporal discretization and Legendre–Chebyshev pseudo-spectral method (LC–PSM) for the space discretization, to solve a class of parabolic integrodifferential equations subject to nonlocal boundary conditions. The approach proposed in this paper is based on Galerkin formulation and Legendre polynomials. Results on stability and convergence are established. Numerical tests are presented to support theoretical results and to demonstrate the accuracy and effectiveness of the proposed method
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ISSN:2193-5343
2193-5351
2193-5351
DOI:10.1007/s40065-022-00371-3