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

Document Type : Research Article

Authors

• A.R. Soheili ¹
• M. Arab Ameri ²
• M. Barfeie ²

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

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

10.22067/ijnao.v5i1.32882

Abstract

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

Keywords

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

20.1001.1.24236977.2015.5.1.4.9

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