A Hermite Collocation Method for the Approximate Solutions of High-Order Linear Fredholm Integro-Differential Equations


Akgonullu N., ŞAHİN N., Sezer M.

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, vol.27, no.6, pp.1707-1721, 2011 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 27 Issue: 6
  • Publication Date: 2011
  • Doi Number: 10.1002/num.20604
  • Journal Name: NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1707-1721
  • Keywords: collocation method, Fredholm integro-differential equations, Hermite polynomials, Hermite series, NUMERICAL-SOLUTION, INTEGRAL-EQUATIONS, DIFFERENCE-EQUATIONS, POLYNOMIAL SOLUTIONS, TAU-METHOD, 2ND KIND, TAYLOR, TERMS
  • Gazi University Affiliated: Yes

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. (C) 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 1707-1721, 2011