Finite difference approach for variable order reaction–subdiffusion equations
Abstract The fractional reaction–subdiffusion equation is one of the most famous subdiffusion equations. These equations are widely used in recent years to simulate many physical phenomena. In this paper, we consider a new version of such equations, namely the variable order linear and nonlinear rea...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2018-11-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-018-1862-x |
| _version_ | 1798043289259081728 |
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| author | M. Adel |
| author_facet | M. Adel |
| author_sort | M. Adel |
| collection | DOAJ |
| description | Abstract The fractional reaction–subdiffusion equation is one of the most famous subdiffusion equations. These equations are widely used in recent years to simulate many physical phenomena. In this paper, we consider a new version of such equations, namely the variable order linear and nonlinear reaction–subdiffusion equation. A numerical study is introduced using the weighted average methods for the variable order linear and nonlinear reaction–subdiffusion equations. A stability analysis of the proposed method is given by a recently proposed procedure similar to the standard John von Neumann stability analysis. The paper is ended with the results of numerical examples that support the theoretical analysis. |
| first_indexed | 2024-04-11T22:47:16Z |
| format | Article |
| id | doaj.art-7b10619b8c4246698cd04d05d7dde64d |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-04-11T22:47:16Z |
| publishDate | 2018-11-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-7b10619b8c4246698cd04d05d7dde64d2022-12-22T03:58:43ZengSpringerOpenAdvances in Difference Equations1687-18472018-11-012018111210.1186/s13662-018-1862-xFinite difference approach for variable order reaction–subdiffusion equationsM. Adel0Department of Mathematics, Faculty of Science, Cairo UniversityAbstract The fractional reaction–subdiffusion equation is one of the most famous subdiffusion equations. These equations are widely used in recent years to simulate many physical phenomena. In this paper, we consider a new version of such equations, namely the variable order linear and nonlinear reaction–subdiffusion equation. A numerical study is introduced using the weighted average methods for the variable order linear and nonlinear reaction–subdiffusion equations. A stability analysis of the proposed method is given by a recently proposed procedure similar to the standard John von Neumann stability analysis. The paper is ended with the results of numerical examples that support the theoretical analysis.http://link.springer.com/article/10.1186/s13662-018-1862-xWeighted average finite difference approximationsVariable order linear and nonlinear reaction–subdiffusion equationStability analysisNumerical example |
| spellingShingle | M. Adel Finite difference approach for variable order reaction–subdiffusion equations Advances in Difference Equations Weighted average finite difference approximations Variable order linear and nonlinear reaction–subdiffusion equation Stability analysis Numerical example |
| title | Finite difference approach for variable order reaction–subdiffusion equations |
| title_full | Finite difference approach for variable order reaction–subdiffusion equations |
| title_fullStr | Finite difference approach for variable order reaction–subdiffusion equations |
| title_full_unstemmed | Finite difference approach for variable order reaction–subdiffusion equations |
| title_short | Finite difference approach for variable order reaction–subdiffusion equations |
| title_sort | finite difference approach for variable order reaction subdiffusion equations |
| topic | Weighted average finite difference approximations Variable order linear and nonlinear reaction–subdiffusion equation Stability analysis Numerical example |
| url | http://link.springer.com/article/10.1186/s13662-018-1862-x |
| work_keys_str_mv | AT madel finitedifferenceapproachforvariableorderreactionsubdiffusionequations |