Table of Contents
International Journal of Computational Mathematics
Volume 2014 (2014), Article ID 671965, 9 pages
http://dx.doi.org/10.1155/2014/671965
Research Article

Solving Operator Equation Based on Expansion Approach

1Department of Applied Mathematics, Faculty of Mathematics, K. N. Toosi University of Technology, P.O. Box 16315-1618, Tehran, Iran
2Department of Mathematics, Ilam University, Ilam, Iran

Received 19 May 2014; Accepted 21 August 2014; Published 7 September 2014

Academic Editor: Yaohang Li

Copyright © 2014 A. Aminataei et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

To date, researchers usually use spectral and pseudospectral methods for only numerical approximation of ordinary and partial differential equations and also based on polynomial basis. But the principal importance of this paper is to develop the expansion approach based on general basis functions (in particular case polynomial basis) for solving general operator equations, wherein the particular cases of our development are integral equations, ordinary differential equations, difference equations, partial differential equations, and fractional differential equations. In other words, this paper presents the expansion approach for solving general operator equations in the form , with respect to boundary condition , where , and are linear, nonlinear, and boundary operators, respectively, related to a suitable Hilbert space, is the domain of approximation, is an arbitrary constant, and is an arbitrary function. Also the other importance of this paper is to introduce the general version of pseudospectral method based on general interpolation problem. Finally some experiments show the accuracy of our development and the error analysis is presented in norm.