Journal of Applied Mathematics
Volume 2012 (2012), Article ID 125926, 17 pages
http://dx.doi.org/10.1155/2012/125926
Research Article

Convergence and Stability in Collocation Methods of Equation

Han Yan,1 Shufang Ma,2 Yanbin Liu,1 and Hongquan Sun1

1School of Mathematical Sciences, Heilongjiang University, Harbin 150080, China
2Department of Mathematics, Northeast Forest University, Harbin 150040, China

Received 13 August 2012; Accepted 4 October 2012

Academic Editor: J. C. Butcher

Copyright © 2012 Han Yan 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

This paper is concerned with the convergence, global superconvergence, local superconvergence, and stability of collocation methods for . The optimal convergence order and superconvergence order are obtained, and the stability regions for the collocation methods are determined. The conditions that the analytic stability region is contained in the numerical stability region are obtained, and some numerical experiments are given.