Error analysis of a meshless weak form method based on radial point interpolation technique for Sivashinsky equation arising in the alloy solidification problem
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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.
论文关键词:41A30,65M99,65N99,Sivashinsky equation,Meshless weak form methods,Radial point interpolation technique,Error estimate,Stability,Convergence analysis,Nonlinear biharmonic equation,Alloy solidification problem
论文评审过程:Received 20 February 2017, Revised 31 May 2017, Available online 29 June 2017, Version of Record 18 July 2017.
论文官网地址:https://doi.org/10.1016/j.cam.2017.06.022