A Direct Meshless Method for Solving Two-Dimensional Second-Order Hyperbolic Telegraph Equations
In this paper, a direct meshless method (DMM), which is based on the radial basis function, is developed to the numerical solution of the two-dimensional second-order hyperbolic telegraph equations. Since these hyperbolic telegraph equations are time dependent, we present two schemes for the basis f...
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| Language: | English |
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Wiley
2020-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2020/8832197 |
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| author | Fuzhang Wang Enran Hou |
| author_facet | Fuzhang Wang Enran Hou |
| author_sort | Fuzhang Wang |
| collection | DOAJ |
| description | In this paper, a direct meshless method (DMM), which is based on the radial basis function, is developed to the numerical solution of the two-dimensional second-order hyperbolic telegraph equations. Since these hyperbolic telegraph equations are time dependent, we present two schemes for the basis functions from radial and nonradial aspects. The first scheme is fulfilled by considering time variable as normal space variable to construct an “isotropic” space-time radial basis function. The other scheme considered a realistic relationship between space variable and time variable which is not radial. The time-dependent variable is treated regularly during the whole solution process and the hyperbolic telegraph equations can be solved in a direct way. Numerical experiments performed with the proposed numerical scheme for several two-dimensional second-order hyperbolic telegraph equations are presented with some discussions, which show that the DMM solutions are converging very fast in comparison with the various existing numerical methods. |
| format | Article |
| id | doaj-art-d0f6d5e522b748b398d414128dd8fed3 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-d0f6d5e522b748b398d414128dd8fed32025-02-03T06:46:58ZengWileyJournal of Mathematics2314-46292314-47852020-01-01202010.1155/2020/88321978832197A Direct Meshless Method for Solving Two-Dimensional Second-Order Hyperbolic Telegraph EquationsFuzhang Wang0Enran Hou1School of Mathematical and Statistics, Xuzhou University of Technology, Xuzhou 221018, Jiangsu, ChinaCollege of Mathematics, Huaibei Normal University, Huaibei 235000, ChinaIn this paper, a direct meshless method (DMM), which is based on the radial basis function, is developed to the numerical solution of the two-dimensional second-order hyperbolic telegraph equations. Since these hyperbolic telegraph equations are time dependent, we present two schemes for the basis functions from radial and nonradial aspects. The first scheme is fulfilled by considering time variable as normal space variable to construct an “isotropic” space-time radial basis function. The other scheme considered a realistic relationship between space variable and time variable which is not radial. The time-dependent variable is treated regularly during the whole solution process and the hyperbolic telegraph equations can be solved in a direct way. Numerical experiments performed with the proposed numerical scheme for several two-dimensional second-order hyperbolic telegraph equations are presented with some discussions, which show that the DMM solutions are converging very fast in comparison with the various existing numerical methods.http://dx.doi.org/10.1155/2020/8832197 |
| spellingShingle | Fuzhang Wang Enran Hou A Direct Meshless Method for Solving Two-Dimensional Second-Order Hyperbolic Telegraph Equations Journal of Mathematics |
| title | A Direct Meshless Method for Solving Two-Dimensional Second-Order Hyperbolic Telegraph Equations |
| title_full | A Direct Meshless Method for Solving Two-Dimensional Second-Order Hyperbolic Telegraph Equations |
| title_fullStr | A Direct Meshless Method for Solving Two-Dimensional Second-Order Hyperbolic Telegraph Equations |
| title_full_unstemmed | A Direct Meshless Method for Solving Two-Dimensional Second-Order Hyperbolic Telegraph Equations |
| title_short | A Direct Meshless Method for Solving Two-Dimensional Second-Order Hyperbolic Telegraph Equations |
| title_sort | direct meshless method for solving two dimensional second order hyperbolic telegraph equations |
| url | http://dx.doi.org/10.1155/2020/8832197 |
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