Generalized Finite Difference Method for Solving Stochastic Diffusion Equations
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912128812711936 |
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| author | Mojarrad, Faezeh Nassajian |
| author_facet | Mojarrad, Faezeh Nassajian |
| contents | Stochastic diffusion equations are crucial for modeling a range of physical phenomena influenced by uncertainties. We introduce the generalized finite difference method for solving these equations. Then, we examine its consistency, stability and convergence in mean-square, showing that the proposed method preserves stability and demonstrates favorable convergence characteristics under suitable assumptions. In order to validate the methodology, we present numerical results in one-, two-, and three-dimensional space domains. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_14333 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generalized Finite Difference Method for Solving Stochastic Diffusion Equations Mojarrad, Faezeh Nassajian Numerical Analysis Stochastic diffusion equations are crucial for modeling a range of physical phenomena influenced by uncertainties. We introduce the generalized finite difference method for solving these equations. Then, we examine its consistency, stability and convergence in mean-square, showing that the proposed method preserves stability and demonstrates favorable convergence characteristics under suitable assumptions. In order to validate the methodology, we present numerical results in one-, two-, and three-dimensional space domains. |
| title | Generalized Finite Difference Method for Solving Stochastic Diffusion Equations |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2411.14333 |