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Chebyshev polynomial approximation for high‐order partial differential equations with complicated conditions
Author(s) -
AkyüzDascioglu Aysegül
Publication year - 2009
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20362
Subject(s) - mathematics , chebyshev equation , chebyshev nodes , chebyshev polynomials , chebyshev iteration , chebyshev pseudospectral method , orthogonal collocation , collocation method , partial differential equation , algebraic equation , chebyshev filter , mathematical analysis , matrix (chemical analysis) , coefficient matrix , polynomial , partial derivative , equioscillation theorem , differential equation , nonlinear system , classical orthogonal polynomials , ordinary differential equation , orthogonal polynomials , gegenbauer polynomials , materials science , quantum mechanics , composite material , eigenvalues and eigenvectors , physics
In this article, a new method is presented for the solution of high‐order linear partial differential equations (PDEs) with variable coefficients under the most general conditions. The method is based on the approximation by the truncated double Chebyshev series. PDE and conditions are transformed into the matrix equations, which corresponds to a system of linear algebraic equations with the unknown Chebyshev coefficients, via Chebyshev collocation points. Combining these matrix equations and then solving the system yields the Chebyshev coefficients of the solution function. Some numerical results are included to demonstrate the validity and applicability of the method. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009