Parameter Estimation for a Type of Fractional Diffusion Equation Based on Compact Difference Scheme
Numerical solution and parameter estimation for a type of fractional diffusion equation are considered. Firstly, the symmetrical compact difference scheme is applied to solve the forward problem of the fractional diffusion equation. The stability and convergence of the symmetrical difference scheme...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-03-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/14/3/560 |
| _version_ | 1797441536010485760 |
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| author | Wei Gu Fang Wei Min Li |
| author_facet | Wei Gu Fang Wei Min Li |
| author_sort | Wei Gu |
| collection | DOAJ |
| description | Numerical solution and parameter estimation for a type of fractional diffusion equation are considered. Firstly, the symmetrical compact difference scheme is applied to solve the forward problem of the fractional diffusion equation. The stability and convergence of the symmetrical difference scheme are presented. Then, the Bayesian method is considered to estimate the unknown fractional order <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> of the fractional diffusion equation model. To validate the efficiency of the symmetrical numerical scheme and the estimation method, some simulation tests are considered. The simulation results demonstrate the accuracy of the compact difference scheme and show that the proposed estimation algorithm can provide effective statistical characteristics of the parameter. |
| first_indexed | 2024-03-09T12:24:34Z |
| format | Article |
| id | doaj.art-2afd432487dc47c7bcec2137de61d033 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T12:24:34Z |
| publishDate | 2022-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-2afd432487dc47c7bcec2137de61d0332023-11-30T22:36:20ZengMDPI AGSymmetry2073-89942022-03-0114356010.3390/sym14030560Parameter Estimation for a Type of Fractional Diffusion Equation Based on Compact Difference SchemeWei Gu0Fang Wei1Min Li2School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan 430073, ChinaSchool of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan 430073, ChinaSchool of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, ChinaNumerical solution and parameter estimation for a type of fractional diffusion equation are considered. Firstly, the symmetrical compact difference scheme is applied to solve the forward problem of the fractional diffusion equation. The stability and convergence of the symmetrical difference scheme are presented. Then, the Bayesian method is considered to estimate the unknown fractional order <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> of the fractional diffusion equation model. To validate the efficiency of the symmetrical numerical scheme and the estimation method, some simulation tests are considered. The simulation results demonstrate the accuracy of the compact difference scheme and show that the proposed estimation algorithm can provide effective statistical characteristics of the parameter.https://www.mdpi.com/2073-8994/14/3/560compact finite difference schemefractional diffusion equationBayesian methodfractional order |
| spellingShingle | Wei Gu Fang Wei Min Li Parameter Estimation for a Type of Fractional Diffusion Equation Based on Compact Difference Scheme Symmetry compact finite difference scheme fractional diffusion equation Bayesian method fractional order |
| title | Parameter Estimation for a Type of Fractional Diffusion Equation Based on Compact Difference Scheme |
| title_full | Parameter Estimation for a Type of Fractional Diffusion Equation Based on Compact Difference Scheme |
| title_fullStr | Parameter Estimation for a Type of Fractional Diffusion Equation Based on Compact Difference Scheme |
| title_full_unstemmed | Parameter Estimation for a Type of Fractional Diffusion Equation Based on Compact Difference Scheme |
| title_short | Parameter Estimation for a Type of Fractional Diffusion Equation Based on Compact Difference Scheme |
| title_sort | parameter estimation for a type of fractional diffusion equation based on compact difference scheme |
| topic | compact finite difference scheme fractional diffusion equation Bayesian method fractional order |
| url | https://www.mdpi.com/2073-8994/14/3/560 |
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