A Hermite collocation method for the approximate solutions of high-order linear Fredholm integro-differential equations


Akgönüllü N., Şahin N. , Sezer M.

Numerical Methods for Partial Differential Equations, vol.27, no.6, pp.1707-1721, 2011 (Journal Indexed in SCI Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 27 Issue: 6
  • Publication Date: 2011
  • Doi Number: 10.1002/num.20604
  • Title of Journal : Numerical Methods for Partial Differential Equations
  • Page Numbers: pp.1707-1721

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.