Error analysis of a meshless weak form method based on radial point interpolation technique for Sivashinsky equation arising in the alloy solidification problem

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:327

Article

Ilati, Mohammad¹  Dehghan, Mehdi¹ 

[1] Amirkabir Univ Technol, Fac Math & Comp Sci, Dept Appl Math, 424 Hafez Ave, Tehran, Iran

关键词: Sivashinsky equation;    Meshless weak form methods;    Radial point interpolation technique;    Error estimate;    Stability;    Convergence analysis;    Nonlinear biharmonic equation;    Alloy solidification problem;   

DOI  :  10.1016/j.cam.2017.06.022

来源: Elsevier

【 摘 要 】

In this paper, meshless weak form techniques are applied to find the numerical solution of nonlinear biharmonic Sivashinsky equation arising in the alloy solidification problem. Stability and convergence analysis of time-discrete scheme are proved. An error analysis of meshless global weak form method based on radial point interpolation technique is proposed for this nonlinear biharmonic equation. In addition, a comparison between meshless global and local weak form methods is done from the perspective of accuracy and efficiency. The main purpose of this paper is to show that the meshless weak form techniques can be used for solving the nonlinear biharmonic partial differential equations especially Sivashinsky equation. The numerical results confirm the good efficiency of the proposed methods for solving this nonlinear biharmonic model. (C) 2017 Elsevier B.V. All rights reserved.

【 授权许可】

Free