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Solving high‐order linear differential equations by a Legendre matrix method based on hybrid Legendre and Taylor polynomials
Author(s) -
Sezer Mehmet,
Gülsu Mustafa
Publication year - 2010
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.20450
Subject(s) - legendre polynomials , mathematics , taylor series , associated legendre polynomials , legendre wavelet , legendre function , legendre's equation , classical orthogonal polynomials , mathematical analysis , partial derivative , variable (mathematics) , matrix (chemical analysis) , taylor's theorem , differential equation , jacobi polynomials , gegenbauer polynomials , orthogonal polynomials , computer science , discrete wavelet transform , materials science , wavelet transform , artificial intelligence , wavelet , composite material
A numerical method for solving the high‐order linear differential equations with variable coefficients under the mixed conditions is presented. The method is based on the hybrid Legendre and Taylor polynomials. The solution is obtained in terms of Legendre polynomials. Comparison of the present solution is made with the existing solution and excellent agreement is noted. Illustrative examples are included to demonstrate the validity and applicability of the technique. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010