Error analysis of Legendre-Galerkin spectral method for a parabolic equation with Dirichlet-Type non-local boundary conditions

An efficient Legendre-Galerkin spectral method and its error analysis for a one-dimensional parabolic equation with Dirichlet-type non-local boundary conditions are presented in this paper. The spatial discretization is based on Galerkin formulation and the Legendre orthogonal polynomials, while the...

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Published inMathematical modelling and analysis Vol. 26; no. 2; pp. 287 - 303
Main Authors Chattouh, Abdeldjalil, Saoudi, Khaled
Format Journal Article
LanguageEnglish
Published Vilnius Vilnius Gediminas Technical University 26.05.2021
Subjects
Boundary conditions
Boundary value problems
Differential equations, Partial
Dirichlet problem
Discretization
Error analysis
error estimate
Finite difference method
Galerkin method
Mathematical analysis
Mathematical research
non-local boundary conditions
Parabola
parabolic equation
Polynomials
Spectra
Spectral methods
Algeria
error estimate
spectral methods
Galerkin method
non-local boundary conditions
parabolic equation
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Abstract An efficient Legendre-Galerkin spectral method and its error analysis for a one-dimensional parabolic equation with Dirichlet-type non-local boundary conditions are presented in this paper. The spatial discretization is based on Galerkin formulation and the Legendre orthogonal polynomials, while the time derivative is discretized by using the symmetric Euler finite difference schema. The stability and convergence of the semi-discrete spectral approximation are rigorously set up by following a novel approach to overcome difficulties caused by the non-locality of the boundary condition. Several numerical tests are included to confirm the efficacy of the proposed method and to support the theoretical results.
AbstractList An efficient Legendre-Galerkin spectral method and its error analysis for a one-dimensional parabolic equation with Dirichlet-type non-local boundary conditions are presented in this paper. The spatial discretization is based on Galerkin formulation and the Legendre orthogonal polynomials, while the time derivative is discretized by using the symmetric Euler finite difference schema. The stability and convergence of the semi-discrete spectral approximation are rigorously set up by following a novel approach to overcome difficulties caused by the non-locality of the boundary condition. Several numerical tests are included to confirm the efficacy of the proposed method and to support the theoretical results.
An efficient Legendre-Galerkin spectral method and its error analysis for a one-dimensional parabolic equation with Dirichlet-type non-local boundary conditions are presented in this paper. The spatial discretization is based on Galerkin formulation and the Legendre orthogonal polynomials, while the time derivative is discretized by using the symmetric Euler finite difference schema. The stability and convergence of the semi-discrete spectral approximation are rigorously set up by following a novel approach to overcome difficulties caused by the non-locality of the boundary condition. Several numerical tests are included to confirm the efficacy of the proposed method and to support the theoretical results. Keywords: spectral methods, Galerkin method, parabolic equation, non-local boundary conditions, error estimate. AMS Subject Classification: 65M70; 65M12; 65N35; 35K20.
Audience Academic
Author Chattouh, Abdeldjalil
Saoudi, Khaled
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SubjectTerms Boundary conditions
Boundary value problems
Differential equations, Partial
Dirichlet problem
Discretization
Error analysis
error estimate
Finite difference method
Galerkin method
Mathematical analysis
Mathematical research
non-local boundary conditions
Parabola
parabolic equation
Polynomials
Spectra
Spectral methods
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Title Error analysis of Legendre-Galerkin spectral method for a parabolic equation with Dirichlet-Type non-local boundary conditions
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