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...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
|
| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/298640 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832545993592143872 |
|---|---|
| author | Tadashi Kawanago |
| author_facet | Tadashi Kawanago |
| author_sort | Tadashi Kawanago |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-6e23f3c5e1004d4a8bfb57d25c2f19a9 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-6e23f3c5e1004d4a8bfb57d25c2f19a92025-02-03T07:24:12ZengWileyJournal 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 |
| spellingShingle | Tadashi Kawanago Error Analysis of Galerkin's Method for Semilinear Equations Journal of Applied Mathematics |
| title | 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_short | Error Analysis of Galerkin's Method for Semilinear Equations |
| title_sort | error analysis of galerkin s method for semilinear equations |
| url | http://dx.doi.org/10.1155/2012/298640 |
| work_keys_str_mv | AT tadashikawanago erroranalysisofgalerkinsmethodforsemilinearequations |