A family of quasi-variable meshes high-resolution compact operator scheme for Burger's-Huxley, and Burger's-Fisher equation
We describe a quasi-variable meshes implicit compact finite-difference discretization having an accuracy of order four in the spatial direction and second-order in the temporal direction for obtaining numerical solution values of generalized Burger’s-Huxley and Burger’s-Fisher equations. The new dif...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Western Libraries
2020-11-01
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| Series: | Mathematics in Applied Sciences and Engineering |
| Subjects: | |
| Online Access: | https://ojs.lib.uwo.ca/index.php/mase/article/view/10837 |
| _version_ | 1819032996838113280 |
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| author | Navnit Jha Madhav Wagley |
| author_facet | Navnit Jha Madhav Wagley |
| author_sort | Navnit Jha |
| collection | DOAJ |
| description | We describe a quasi-variable meshes implicit compact finite-difference discretization having an accuracy of order four in the spatial direction and second-order in the temporal direction for obtaining numerical solution values of generalized Burger’s-Huxley and Burger’s-Fisher equations. The new difference scheme is derived for a general one-dimension quasi-linear parabolic partial differential equation on a quasi-variable meshes network to the extent that the magnitude of local truncation error of the high-order compact scheme remains unchanged in case of uniform meshes network. Practically, quasi-variable meshes high-order compact schemes yield more precise solution compared with uniform meshes high-order schemes of the same magnitude. A detailed exposition of the new scheme has been introduced and discussed the Fourier analysis based stability theory. The computational results with generalized Burger’s-Huxley equation and Burger’s-Fisher equation are obtained using quasi-variable meshes high-order compact scheme and compared with a numerical solution using uniform meshes high-order schemes to demonstrate capability and accuracy. |
| first_indexed | 2024-12-21T07:10:49Z |
| format | Article |
| id | doaj.art-0dee6f7c10a8469082038b33dac20533 |
| institution | Directory Open Access Journal |
| issn | 2563-1926 |
| language | English |
| last_indexed | 2024-12-21T07:10:49Z |
| publishDate | 2020-11-01 |
| publisher | Western Libraries |
| record_format | Article |
| series | Mathematics in Applied Sciences and Engineering |
| spelling | doaj.art-0dee6f7c10a8469082038b33dac205332022-12-21T19:11:59ZengWestern LibrariesMathematics in Applied Sciences and Engineering2563-19262020-11-011428630810.5206/mase/108374977A family of quasi-variable meshes high-resolution compact operator scheme for Burger's-Huxley, and Burger's-Fisher equationNavnit Jha0Madhav Wagley1South Asian UniversitySouth Asian UniversityWe describe a quasi-variable meshes implicit compact finite-difference discretization having an accuracy of order four in the spatial direction and second-order in the temporal direction for obtaining numerical solution values of generalized Burger’s-Huxley and Burger’s-Fisher equations. The new difference scheme is derived for a general one-dimension quasi-linear parabolic partial differential equation on a quasi-variable meshes network to the extent that the magnitude of local truncation error of the high-order compact scheme remains unchanged in case of uniform meshes network. Practically, quasi-variable meshes high-order compact schemes yield more precise solution compared with uniform meshes high-order schemes of the same magnitude. A detailed exposition of the new scheme has been introduced and discussed the Fourier analysis based stability theory. The computational results with generalized Burger’s-Huxley equation and Burger’s-Fisher equation are obtained using quasi-variable meshes high-order compact scheme and compared with a numerical solution using uniform meshes high-order schemes to demonstrate capability and accuracy.https://ojs.lib.uwo.ca/index.php/mase/article/view/10837compact scheme, quasi-variable mesh, generalized burgers-huxley equation, generalized burgers-fisher equation, ilkovič’s equation, stability, maximum-absolute-errors |
| spellingShingle | Navnit Jha Madhav Wagley A family of quasi-variable meshes high-resolution compact operator scheme for Burger's-Huxley, and Burger's-Fisher equation Mathematics in Applied Sciences and Engineering compact scheme, quasi-variable mesh, generalized burgers-huxley equation, generalized burgers-fisher equation, ilkovič’s equation, stability, maximum-absolute-errors |
| title | A family of quasi-variable meshes high-resolution compact operator scheme for Burger's-Huxley, and Burger's-Fisher equation |
| title_full | A family of quasi-variable meshes high-resolution compact operator scheme for Burger's-Huxley, and Burger's-Fisher equation |
| title_fullStr | A family of quasi-variable meshes high-resolution compact operator scheme for Burger's-Huxley, and Burger's-Fisher equation |
| title_full_unstemmed | A family of quasi-variable meshes high-resolution compact operator scheme for Burger's-Huxley, and Burger's-Fisher equation |
| title_short | A family of quasi-variable meshes high-resolution compact operator scheme for Burger's-Huxley, and Burger's-Fisher equation |
| title_sort | family of quasi variable meshes high resolution compact operator scheme for burger s huxley and burger s fisher equation |
| topic | compact scheme, quasi-variable mesh, generalized burgers-huxley equation, generalized burgers-fisher equation, ilkovič’s equation, stability, maximum-absolute-errors |
| url | https://ojs.lib.uwo.ca/index.php/mase/article/view/10837 |
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