Higher-Order Compact Finite Difference for Certain PDEs in Arbitrary Dimensions
In this paper, we first present the expression of a model of a fourth-order compact finite difference (CFD) scheme for the convection diffusion equation with variable convection coefficient. Then, we also obtain the fourth-order CFD schemes of the diffusion equation with variable diffusion coefficie...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2020/8567605 |
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| _version_ | 1832546790827622400 |
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| author | Yan Gao Songlin Liu |
| author_facet | Yan Gao Songlin Liu |
| author_sort | Yan Gao |
| collection | DOAJ |
| description | In this paper, we first present the expression of a model of a fourth-order compact finite difference (CFD) scheme for the convection diffusion equation with variable convection coefficient. Then, we also obtain the fourth-order CFD schemes of the diffusion equation with variable diffusion coefficients. In addition, a fine description of the sixth-order CFD schemes is also developed for equations with constant coefficients, which is used to discuss certain partial differential equations (PDEs) with arbitrary dimensions. In this paper, various ways of numerical test calculations are prepared to evaluate performance of the fourth-order CFD and sixth-order CFD schemes, respectively, and the empirical results are proved to verify the effectiveness of the schemes in this paper. |
| format | Article |
| id | doaj-art-25e52e1dac9446f6ac3c6f695dce239d |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-25e52e1dac9446f6ac3c6f695dce239d2025-02-03T06:46:58ZengWileyJournal of Function Spaces2314-88962314-88882020-01-01202010.1155/2020/85676058567605Higher-Order Compact Finite Difference for Certain PDEs in Arbitrary DimensionsYan Gao0Songlin Liu1Department of Information Engineering, Wuhan Business University, Wuhan 430056, ChinaFaculty of Mathematics and Statistics, Key Laboratory of Applied Mathematics of Hubei Province, Hubei University, Wuhan 430062, ChinaIn this paper, we first present the expression of a model of a fourth-order compact finite difference (CFD) scheme for the convection diffusion equation with variable convection coefficient. Then, we also obtain the fourth-order CFD schemes of the diffusion equation with variable diffusion coefficients. In addition, a fine description of the sixth-order CFD schemes is also developed for equations with constant coefficients, which is used to discuss certain partial differential equations (PDEs) with arbitrary dimensions. In this paper, various ways of numerical test calculations are prepared to evaluate performance of the fourth-order CFD and sixth-order CFD schemes, respectively, and the empirical results are proved to verify the effectiveness of the schemes in this paper.http://dx.doi.org/10.1155/2020/8567605 |
| spellingShingle | Yan Gao Songlin Liu Higher-Order Compact Finite Difference for Certain PDEs in Arbitrary Dimensions Journal of Function Spaces |
| title | Higher-Order Compact Finite Difference for Certain PDEs in Arbitrary Dimensions |
| title_full | Higher-Order Compact Finite Difference for Certain PDEs in Arbitrary Dimensions |
| title_fullStr | Higher-Order Compact Finite Difference for Certain PDEs in Arbitrary Dimensions |
| title_full_unstemmed | Higher-Order Compact Finite Difference for Certain PDEs in Arbitrary Dimensions |
| title_short | Higher-Order Compact Finite Difference for Certain PDEs in Arbitrary Dimensions |
| title_sort | higher order compact finite difference for certain pdes in arbitrary dimensions |
| url | http://dx.doi.org/10.1155/2020/8567605 |
| work_keys_str_mv | AT yangao higherordercompactfinitedifferenceforcertainpdesinarbitrarydimensions AT songlinliu higherordercompactfinitedifferenceforcertainpdesinarbitrarydimensions |