Rational approximation to the fractional Laplacian operator in reaction-diffusion problems
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2016
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| _version_ | 1866909138063196160 |
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| author | Aceto, Lidia Novati, Paolo |
| author_facet | Aceto, Lidia Novati, Paolo |
| contents | This paper provides a new numerical strategy to solve fractional in space reaction-diffusion equations on bounded domains under homogeneous Dirichlet boundary conditions. Using the matrix transform method the fractional Laplacian operator is replaced by a matrix which, in general, is dense. The approach here presented is based on the approximation of this matrix by the product of two suitable banded matrices. This leads to a semi-linear initial value problem in which the matrices involved are sparse. Numerical results are presented to verify the effectiveness of the proposed solution strategy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1607_04166 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | Rational approximation to the fractional Laplacian operator in reaction-diffusion problems Aceto, Lidia Novati, Paolo Numerical Analysis 65F60, 35R11, 65D32 This paper provides a new numerical strategy to solve fractional in space reaction-diffusion equations on bounded domains under homogeneous Dirichlet boundary conditions. Using the matrix transform method the fractional Laplacian operator is replaced by a matrix which, in general, is dense. The approach here presented is based on the approximation of this matrix by the product of two suitable banded matrices. This leads to a semi-linear initial value problem in which the matrices involved are sparse. Numerical results are presented to verify the effectiveness of the proposed solution strategy. |
| title | Rational approximation to the fractional Laplacian operator in reaction-diffusion problems |
| topic | Numerical Analysis 65F60, 35R11, 65D32 |
| url | https://arxiv.org/abs/1607.04166 |