RBFs meshless method of lines based on adaptive nodes for Burgers' equations

Iranian Journal of Numerical Analysis and Optimization

مقاله 3، دوره 5، شماره 1 - شماره پیاپی 7، تیر 2015، صفحه 49-61   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.v5i1.32882

نویسندگان

A.R. Soheili^{* 1}؛ M. Arab Ameri²؛ M. Barfeie²

¹The Center of Excellence on Modeling and Control Systems, Department of Applied Math- ematics, Ferdowsi University of Mashhad, Mashhad, Iran.

²Faculty of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran.

چکیده

We introduce a RBFs mesheless method of lines that decomposes the interior and boundary centers to obtain the numerical solution of the time dependent PDEs. Then, the method is applied with an adaptive algorithm to obtain the numerical solution of one dimensional problem. We show that in the problems in which the solutions contain region with rapid variation, the adaptive RBFs methods are successful so that the PDE solution can be approximated well with a small number of basis functions. The method is described in detail, and computational experiments are performed for one-dimensional Burgers' equations

کلیدواژه‌ها

Method of Lines؛ Radial basis functions؛ Adaptive Method؛ Burgers' Equations

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