Direct and indirect approximations to positive solution for a nonlinear reaction-diffusion problem. II. Indirect approximation
In this paper we continue the study initiated in our previous work [3] and design a projection-like algorithm to approximate a hyperbolic unstable "point''. This "point'' is in fact the positive solution of the reaction-diffusion problem considered in [3] and the algori...
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| Format: | Article |
| Language: | English |
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Publishing House of the Romanian Academy
2002-08-01
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| Series: | Journal of Numerical Analysis and Approximation Theory |
| Subjects: | |
| Online Access: | https://www.ictp.acad.ro/jnaat/journal/article/view/720 |
| _version_ | 1828543854766194688 |
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| author | Călin Ioan Gheorghiu Damian Trif |
| author_facet | Călin Ioan Gheorghiu Damian Trif |
| author_sort | Călin Ioan Gheorghiu |
| collection | DOAJ |
| description | In this paper we continue the study initiated in our previous work [3] and design a projection-like algorithm to approximate a hyperbolic unstable "point''. This "point'' is in fact the positive solution of the reaction-diffusion problem considered in [3] and the algorithm modifies a finite difference (Euler)-finite elements scheme by incorporating the independence of the length of the domain condition. The numerical results are in good agreement with those obtained by direct methods as well as with those reported in [2], where the problem is solved in a Hamiltonian setting. At the same time we improve our previous results reported in [3]. |
| first_indexed | 2024-12-12T02:21:09Z |
| format | Article |
| id | doaj.art-28f3d1e75ebe4ed195c56e0857d7d7c1 |
| institution | Directory Open Access Journal |
| issn | 2457-6794 2501-059X |
| language | English |
| last_indexed | 2024-12-12T02:21:09Z |
| publishDate | 2002-08-01 |
| publisher | Publishing House of the Romanian Academy |
| record_format | Article |
| series | Journal of Numerical Analysis and Approximation Theory |
| spelling | doaj.art-28f3d1e75ebe4ed195c56e0857d7d7c12022-12-22T00:41:41ZengPublishing House of the Romanian AcademyJournal of Numerical Analysis and Approximation Theory2457-67942501-059X2002-08-01312Direct and indirect approximations to positive solution for a nonlinear reaction-diffusion problem. II. Indirect approximationCălin Ioan Gheorghiu0Damian Trif1Tiberiu Popoviciu, Institute of Numerical Analysis, Romanian Academy“Babes-Bolyai” University, Cluj-Napoca, RomaniaIn this paper we continue the study initiated in our previous work [3] and design a projection-like algorithm to approximate a hyperbolic unstable "point''. This "point'' is in fact the positive solution of the reaction-diffusion problem considered in [3] and the algorithm modifies a finite difference (Euler)-finite elements scheme by incorporating the independence of the length of the domain condition. The numerical results are in good agreement with those obtained by direct methods as well as with those reported in [2], where the problem is solved in a Hamiltonian setting. At the same time we improve our previous results reported in [3].https://www.ictp.acad.ro/jnaat/journal/article/view/720nonlinear reaction-diffusionpositive solutionconserved integralprojection-like methodf.e.m.finite elements-finite differences method |
| spellingShingle | Călin Ioan Gheorghiu Damian Trif Direct and indirect approximations to positive solution for a nonlinear reaction-diffusion problem. II. Indirect approximation Journal of Numerical Analysis and Approximation Theory nonlinear reaction-diffusion positive solution conserved integral projection-like method f.e.m. finite elements-finite differences method |
| title | Direct and indirect approximations to positive solution for a nonlinear reaction-diffusion problem. II. Indirect approximation |
| title_full | Direct and indirect approximations to positive solution for a nonlinear reaction-diffusion problem. II. Indirect approximation |
| title_fullStr | Direct and indirect approximations to positive solution for a nonlinear reaction-diffusion problem. II. Indirect approximation |
| title_full_unstemmed | Direct and indirect approximations to positive solution for a nonlinear reaction-diffusion problem. II. Indirect approximation |
| title_short | Direct and indirect approximations to positive solution for a nonlinear reaction-diffusion problem. II. Indirect approximation |
| title_sort | direct and indirect approximations to positive solution for a nonlinear reaction diffusion problem ii indirect approximation |
| topic | nonlinear reaction-diffusion positive solution conserved integral projection-like method f.e.m. finite elements-finite differences method |
| url | https://www.ictp.acad.ro/jnaat/journal/article/view/720 |
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