Redistribution of Nodes with Two Constraints in Meshless Method of Line to Time-Dependent Partial Differential Equations
Meshless method of line is a powerful device to solve time-dependent partial differential equations. In integrating step, choosing a suitable set of points, such as adaptive nodes in spatial domain, can be useful, although in some cases this can cause ill-conditioning. In this paper, to produce smoo...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2015/762034 |
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| author | Jafar Biazar Mohammad Hosami |
| author_facet | Jafar Biazar Mohammad Hosami |
| author_sort | Jafar Biazar |
| collection | DOAJ |
| description | Meshless method of line is a powerful device to solve time-dependent partial differential equations. In integrating step, choosing a suitable set of points, such as adaptive nodes in spatial domain, can be useful, although in some cases this can cause ill-conditioning. In this paper, to produce smooth adaptive points in each step of the method, two constraints are enforced in Equidistribution algorithm. These constraints lead to two different meshes known as quasi-uniform and locally bounded meshes. These avoid the ill-conditioning in applying radial basis functions. Moreover, to generate more smooth adaptive meshes another modification is investigated, such as using modified arc-length monitor function in Equidistribution algorithm. Influence of them in growing the accuracy is investigated by some numerical examples. The results of consideration of two constraints are compared with each other and also with uniform meshes. |
| format | Article |
| id | doaj-art-4a12c259953b40fb9b2b8d244024cda9 |
| institution | Kabale University |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-4a12c259953b40fb9b2b8d244024cda92025-02-03T05:52:32ZengWileyInternational Journal of Differential Equations1687-96431687-96512015-01-01201510.1155/2015/762034762034Redistribution of Nodes with Two Constraints in Meshless Method of Line to Time-Dependent Partial Differential EquationsJafar Biazar0Mohammad Hosami1Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, P.O. Box 41335-1914, Rasht 4193822697, IranDepartment of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, P.O. Box 41335-1914, Rasht 4193822697, IranMeshless method of line is a powerful device to solve time-dependent partial differential equations. In integrating step, choosing a suitable set of points, such as adaptive nodes in spatial domain, can be useful, although in some cases this can cause ill-conditioning. In this paper, to produce smooth adaptive points in each step of the method, two constraints are enforced in Equidistribution algorithm. These constraints lead to two different meshes known as quasi-uniform and locally bounded meshes. These avoid the ill-conditioning in applying radial basis functions. Moreover, to generate more smooth adaptive meshes another modification is investigated, such as using modified arc-length monitor function in Equidistribution algorithm. Influence of them in growing the accuracy is investigated by some numerical examples. The results of consideration of two constraints are compared with each other and also with uniform meshes.http://dx.doi.org/10.1155/2015/762034 |
| spellingShingle | Jafar Biazar Mohammad Hosami Redistribution of Nodes with Two Constraints in Meshless Method of Line to Time-Dependent Partial Differential Equations International Journal of Differential Equations |
| title | Redistribution of Nodes with Two Constraints in Meshless Method of Line to Time-Dependent Partial Differential Equations |
| title_full | Redistribution of Nodes with Two Constraints in Meshless Method of Line to Time-Dependent Partial Differential Equations |
| title_fullStr | Redistribution of Nodes with Two Constraints in Meshless Method of Line to Time-Dependent Partial Differential Equations |
| title_full_unstemmed | Redistribution of Nodes with Two Constraints in Meshless Method of Line to Time-Dependent Partial Differential Equations |
| title_short | Redistribution of Nodes with Two Constraints in Meshless Method of Line to Time-Dependent Partial Differential Equations |
| title_sort | redistribution of nodes with two constraints in meshless method of line to time dependent partial differential equations |
| url | http://dx.doi.org/10.1155/2015/762034 |
| work_keys_str_mv | AT jafarbiazar redistributionofnodeswithtwoconstraintsinmeshlessmethodoflinetotimedependentpartialdifferentialequations AT mohammadhosami redistributionofnodeswithtwoconstraintsinmeshlessmethodoflinetotimedependentpartialdifferentialequations |