A high order method for numerical solution of time-fractional KdV equation by radial basis functions
Abstract A radial basis function method for solving time-fractional KdV equation is presented. The Caputo derivative is approximated by the high order formulas introduced in Buhman (Proc. Edinb. Math. Soc. 36:319–333, 1993). By choosing the centers of radial basis functions as collocation points, in...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2018-02-01
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| Series: | Arabian Journal of Mathematics |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1007/s40065-018-0197-5 |
| _version_ | 1819035724517736448 |
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| author | B. Sepehrian Z. Shamohammadi |
| author_facet | B. Sepehrian Z. Shamohammadi |
| author_sort | B. Sepehrian |
| collection | DOAJ |
| description | Abstract A radial basis function method for solving time-fractional KdV equation is presented. The Caputo derivative is approximated by the high order formulas introduced in Buhman (Proc. Edinb. Math. Soc. 36:319–333, 1993). By choosing the centers of radial basis functions as collocation points, in each time step a nonlinear system of algebraic equations is obtained. A fixed point predictor–corrector method for solving the system is introduced. The efficiency and accuracy of our method are demonstrated through several illustrative examples. By the examples, the experimental convergence order is approximately $$4-\alpha $$ 4-α , where $$\alpha $$ α is the order of time derivative. |
| first_indexed | 2024-12-21T07:54:11Z |
| format | Article |
| id | doaj.art-dfe16b04088c4c448eb7eeca64854e06 |
| institution | Directory Open Access Journal |
| issn | 2193-5343 2193-5351 |
| language | English |
| last_indexed | 2024-12-21T07:54:11Z |
| publishDate | 2018-02-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Arabian Journal of Mathematics |
| spelling | doaj.art-dfe16b04088c4c448eb7eeca64854e062022-12-21T19:11:01ZengSpringerOpenArabian Journal of Mathematics2193-53432193-53512018-02-017430331510.1007/s40065-018-0197-5A high order method for numerical solution of time-fractional KdV equation by radial basis functionsB. Sepehrian0Z. Shamohammadi1Department of Mathematics, Faculty of Science, Arak UniversityDepartment of Mathematics, Faculty of Science, Arak UniversityAbstract A radial basis function method for solving time-fractional KdV equation is presented. The Caputo derivative is approximated by the high order formulas introduced in Buhman (Proc. Edinb. Math. Soc. 36:319–333, 1993). By choosing the centers of radial basis functions as collocation points, in each time step a nonlinear system of algebraic equations is obtained. A fixed point predictor–corrector method for solving the system is introduced. The efficiency and accuracy of our method are demonstrated through several illustrative examples. By the examples, the experimental convergence order is approximately $$4-\alpha $$ 4-α , where $$\alpha $$ α is the order of time derivative.http://link.springer.com/article/10.1007/s40065-018-0197-565D0565M0665N0665N35 |
| spellingShingle | B. Sepehrian Z. Shamohammadi A high order method for numerical solution of time-fractional KdV equation by radial basis functions Arabian Journal of Mathematics 65D05 65M06 65N06 65N35 |
| title | A high order method for numerical solution of time-fractional KdV equation by radial basis functions |
| title_full | A high order method for numerical solution of time-fractional KdV equation by radial basis functions |
| title_fullStr | A high order method for numerical solution of time-fractional KdV equation by radial basis functions |
| title_full_unstemmed | A high order method for numerical solution of time-fractional KdV equation by radial basis functions |
| title_short | A high order method for numerical solution of time-fractional KdV equation by radial basis functions |
| title_sort | high order method for numerical solution of time fractional kdv equation by radial basis functions |
| topic | 65D05 65M06 65N06 65N35 |
| url | http://link.springer.com/article/10.1007/s40065-018-0197-5 |
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