Application of M-matrices theory to numerical investigation of a nonlinear elliptic equation with an integral condition
The iterative methods to solve the system of the difference equations derived from the nonlinear elliptic equation with integral condition are considered. The convergence of these methods is proved using the properties of M-matrices, in particular, the regular splitting of an M-matrix. To our knowle...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Vilnius University Press
2017-07-01
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| Series: | Nonlinear Analysis |
| Subjects: | |
| Online Access: | http://www.zurnalai.vu.lt/nonlinear-analysis/article/view/13380 |
| _version_ | 1819018264846532608 |
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| author | Mifodijus Sapagovas Viktorija Griškonienė Olga Štikonienė |
| author_facet | Mifodijus Sapagovas Viktorija Griškonienė Olga Štikonienė |
| author_sort | Mifodijus Sapagovas |
| collection | DOAJ |
| description | The iterative methods to solve the system of the difference equations derived from the nonlinear elliptic equation with integral condition are considered. The convergence of these methods is proved using the properties of M-matrices, in particular, the regular splitting of an M-matrix. To our knowledge, the theory of M-matrices has not ever been applied to convergence of iterative methods for system of nonlinear difference equations. The main results for the convergence of the iterative methods are obtained by considering the structure of the spectrum of the two-dimensional difference operators with integral condition.
*The research was partially supported by the Research Council of Lithuania (grant No. MIP-047/2014). |
| first_indexed | 2024-12-21T03:16:40Z |
| format | Article |
| id | doaj.art-fab8db092a5840bdafaacbf29b0bc2c2 |
| institution | Directory Open Access Journal |
| issn | 1392-5113 2335-8963 |
| language | English |
| last_indexed | 2024-12-21T03:16:40Z |
| publishDate | 2017-07-01 |
| publisher | Vilnius University Press |
| record_format | Article |
| series | Nonlinear Analysis |
| spelling | doaj.art-fab8db092a5840bdafaacbf29b0bc2c22022-12-21T19:17:49ZengVilnius University PressNonlinear Analysis1392-51132335-89632017-07-0122410.15388/NA.2017.4.5Application of M-matrices theory to numerical investigation of a nonlinear elliptic equation with an integral conditionMifodijus Sapagovas0Viktorija Griškonienė1Olga Štikonienė2Vilnius UniversityVytautas Magnus UniversityVilnius UniversityThe iterative methods to solve the system of the difference equations derived from the nonlinear elliptic equation with integral condition are considered. The convergence of these methods is proved using the properties of M-matrices, in particular, the regular splitting of an M-matrix. To our knowledge, the theory of M-matrices has not ever been applied to convergence of iterative methods for system of nonlinear difference equations. The main results for the convergence of the iterative methods are obtained by considering the structure of the spectrum of the two-dimensional difference operators with integral condition. *The research was partially supported by the Research Council of Lithuania (grant No. MIP-047/2014).http://www.zurnalai.vu.lt/nonlinear-analysis/article/view/13380elliptic equationfinite-difference methodintegral boundary conditioniterative methodeigenvalue problemM-matrix |
| spellingShingle | Mifodijus Sapagovas Viktorija Griškonienė Olga Štikonienė Application of M-matrices theory to numerical investigation of a nonlinear elliptic equation with an integral condition Nonlinear Analysis elliptic equation finite-difference method integral boundary condition iterative method eigenvalue problem M-matrix |
| title | Application of M-matrices theory to numerical investigation of a nonlinear elliptic equation with an integral condition |
| title_full | Application of M-matrices theory to numerical investigation of a nonlinear elliptic equation with an integral condition |
| title_fullStr | Application of M-matrices theory to numerical investigation of a nonlinear elliptic equation with an integral condition |
| title_full_unstemmed | Application of M-matrices theory to numerical investigation of a nonlinear elliptic equation with an integral condition |
| title_short | Application of M-matrices theory to numerical investigation of a nonlinear elliptic equation with an integral condition |
| title_sort | application of m matrices theory to numerical investigation of a nonlinear elliptic equation with an integral condition |
| topic | elliptic equation finite-difference method integral boundary condition iterative method eigenvalue problem M-matrix |
| url | http://www.zurnalai.vu.lt/nonlinear-analysis/article/view/13380 |
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