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A Hermite collocation method for the approximate solutions of high‐order linear Fredholm integro‐differential equations
Author(s) -
Akgönüllü Nilay,
Şahin Niyazi,
Sezer Mehmet
Publication year - 2011
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.20604
Subject(s) - hermite polynomials , mathematics , orthogonal collocation , matrix (chemical analysis) , collocation (remote sensing) , algebraic equation , polynomial , mathematical analysis , collocation method , differential equation , partial differential equation , coefficient matrix , hermite interpolation , ordinary differential equation , nonlinear system , physics , quantum mechanics , geology , composite material , eigenvalues and eigenvectors , materials science , remote sensing
Abstract In this study, a Hermite matrix method is presented to solve high‐order linear Fredholm integro‐differential equations with variable coefficients under the mixed conditions in terms of the Hermite polynomials. The proposed method converts the equation and its conditions to matrix equations, which correspond to a system of linear algebraic equations with unknown Hermite coefficients, by means of collocation points on a finite interval. Then, by solving the matrix equation, the Hermite coefficients and the polynomial approach are obtained. Also, examples that illustrate the pertinent features of the method are presented; the accuracy of the solutions and the error analysis are performed. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 1707–1721, 2011