Chebyshev polynomial solutions of second-order linear partial differential equations
type: Item
instance of: scholarly article
title: Chebyshev polynomial solutions of second-order linear partial differential equations
zbMATH Open document ID: 1029.35055
DOI: 10.1016/S0096-3003(01)00273-9
author: Cenk Keşan
published in: Applied Mathematics and Computation
publication date: 2003-01-28T00:00:00Z
review text: Approximate polynomial solutions to second-order linear PDE with variable coefficients of the following form \[ A(x,y)\frac{\partial^2 u}{\partial x^2}+ B(x,y)\frac{\partial^2 u}{\partial x\partial y}+ C(x,y)\frac{\partial^2 u}{\partial y^2}+ D(x,y)\frac{\partial u}{\partial x}+ E(x,y)\frac{\partial u}{\partial y}+F(x,y)= G(x,y)\tag{*} \] are considered. The proposed method is based on taking the truncated Chebyshev expansions of the unknown function \(u(x,y)=\sum_{r=0}^n \sum_{s=0}^na_{r,s}T_{r,s}(x,y)\), where \(T_{r,s}(x,y)\) are the Chebyshev polynomials defined in [\textit{N. K. Basu}, SIAM J. Numer. Anal. 10, 496-505 (1973; Zbl 0254.41011)] and also of all coefficients of equation (*) and all functions included in the boundary value conditions to equation (*). The original boundary value problem (or initial value problem) is reduced to the system of algebraic equations for determining coefficients \(a_{r,s}\). Three examples are given.
Mathematics Subject Classification ID: 35C10
Mathematics Subject Classification ID: 35G05
zbMATH DE Number: 1861288
zbMATH Keywords: approximate solution
reviewed by: Valery V. Karachik
MaRDI profile type: Publication
cites work: Chebyshev polynomial solutions of linear differential equations
cites work: On Double Chebyshev Series Approximation
cites work: Chebyshev series solution of linear Fredholm integrodifferential equations
cites work: Q3746168
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description: scientific article; zbMATH DE number 1861288