International Journal of Differential Equations

Redistribution of Nodes with Two Constraints in Meshless Method of Line to Time-Dependent Partial Differential Equations

Jafar Biazar and Mohammad Hosami

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Abstract

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.

Article information

Source
Int. J. Differ. Equ., Volume 2015 (2015), Article ID 762034, 8 pages.

Dates
Received: 6 July 2015
Accepted: 19 October 2015
First available in Project Euclid: 20 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.ijde/1484881448

Digital Object Identifier
doi:10.1155/2015/762034

Mathematical Reviews number (MathSciNet)
MR3423584

Zentralblatt MATH identifier
1382.65283

Citation

Biazar, Jafar; Hosami, Mohammad. Redistribution of Nodes with Two Constraints in Meshless Method of Line to Time-Dependent Partial Differential Equations. Int. J. Differ. Equ. 2015 (2015), Article ID 762034, 8 pages. doi:10.1155/2015/762034. https://projecteuclid.org/euclid.ijde/1484881448


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