Variable Shape Parameter Strategy in Local Radial Basis Functions Collocation Method for Solving the 2D Nonlinear Coupled Burgers’ Equations

Hananeh Nojavan, Saeid Abbasbandy and Tofigh Allahviranloo
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Hananeh Nojavan: Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran 14778, Iran
Saeid Abbasbandy: Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran 14778, Iran
Tofigh Allahviranloo: Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran 14778, Iran

Mathematics, 2017, vol. 5, issue 3, 1-21

Abstract: This study aimed at investigating a local radial basis function collocation method (LRBFCM) in the reproducing kernel Hilbert space. This method was, in fact, a meshless one which applied the local sub-clusters of domain nodes for the approximation of the arbitrary field. For time-dependent partial differential equations (PDEs), it would be changed to a system of ordinary differential equations (ODEs). Here, we intended to decrease the error through utilizing variable shape parameter (VSP) strategies. This method was an appropriate way to solve the two-dimensional nonlinear coupled Burgers’ equations comprised of Dirichlet and mixed boundary conditions. Numerical examples indicated that the variable shape parameter strategies were more efficient than constant ones for various values of the Reynolds number.

Keywords: local meshless method; variable shape parameter (VSP); reproducing kernel space; 2D nonlinear coupled Burgers’ equations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2017
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