## International Journal of Differential Equations

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

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

Jafar Biazar and Mohammad Hosami

#### 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