Error Analysis of Galerkin's Method for Semilinear Equations

Error Analysis of Galerkin's Method for Semilinear Equations

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...

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Main Author: Tadashi Kawanago
Format: Article
Language:English
Published: Hindawi Limited 2012-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2012/298640
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spelling doaj-6e23f3c5e1004d4a8bfb57d25c2f19a92020-11-24T20:43:03ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/298640298640Error Analysis of Galerkin's Method for Semilinear EquationsTadashi Kawanago0Department of Mathematics, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, JapanWe 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.http://dx.doi.org/10.1155/2012/298640
collection DOAJ
language English
format Article
sources DOAJ
author Tadashi Kawanago
spellingShingle Tadashi Kawanago
Error Analysis of Galerkin's Method for Semilinear Equations
Journal of Applied Mathematics
author_facet Tadashi Kawanago
author_sort Tadashi Kawanago
title Error Analysis of Galerkin's Method for Semilinear Equations
title_short Error Analysis of Galerkin's Method for Semilinear Equations
title_full Error Analysis of Galerkin's Method for Semilinear Equations
title_fullStr Error Analysis of Galerkin's Method for Semilinear Equations
title_full_unstemmed Error Analysis of Galerkin's Method for Semilinear Equations
title_sort error analysis of galerkin's method for semilinear equations
publisher Hindawi Limited
series Journal of Applied Mathematics
issn 1110-757X
1687-0042
publishDate 2012-01-01
description 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.
url http://dx.doi.org/10.1155/2012/298640
work_keys_str_mv AT tadashikawanago erroranalysisofgalerkinsmethodforsemilinearequations
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