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Journal of Applied Mathematics
Volume 2012, Article ID 298640, 15 pages
http://dx.doi.org/10.1155/2012/298640
Research Article

Error Analysis of Galerkin's Method for Semilinear Equations

Department of Mathematics, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, Japan

Received 7 January 2012; Revised 16 May 2012; Accepted 8 June 2012

Academic Editor: Hui-Shen Shen

Copyright © 2012 Tadashi Kawanago. 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

We establish a general existence result for Galerkin's approximate solutions of abstract semilinear equations and conduct an error analysis. Our results may be regarded as some extension of a precedent work (Schultz 1969). The derivation of our results is, however, different from the discussion in his paper and is essentially based on the convergence theorem of Newton’s method and some techniques for deriving it. Some of our results may be applicable for investigating the quality of numerical verification methods for solutions of ordinary and partial differential equations.