A Computational Meshfree Technique for the Numerical Solution of the Two-Dimensional Coupled Burgers' Equations

Abstract

In this paper we employ a meshfree technique for the numerical solution of the two-dimensional coupled Burgers' equations. Combination of the collocation method using the radial basis functions (RBFs) with first-order accurate forward difference approximation is employed for obtaining a meshfree solution of the problem. Three different types of RBFs are used for this purpose. Performance of the proposed method is successfully tested in terms of various error norms. In the case of non-availability of exact solution, performance of the new method is compared with the existing methods. The elementary stability analysis is established theoretically and is also supported by numerical results.