Numerical solution of coupled 1D Burgers’ equation by employing Barycentric Lagrange interpolation basis function based differential quadrature method

Abstract

The aim of present study is to develop a numerical scheme by using the notion of Barycentric Lagrange interpolation based Differential quadrature method to solve the coupled 1D Burgers’ equation. This method reduced the mentioned partial differential equation into the set of ordinary differential equations, which can be dealt by the SSP-RK43 scheme. The proposed method has been implemented upon the different numerical examples in order to test the accuracy and effectiveness of the proposed method. It is observed that obtained results are in good compatibility with the exact solution and are better than the previous results. The stability of the proposed method is also discussed by using the matrix stability analysis method, which represents that the proposed method is unconditionally stable.

KEYWORD:

• Differential quadrature method
• Barycentric form of Lagrange interpolation polynomial
• SSP-RK 43 scheme
• matrix stability analysis method

Disclosure statement

No potential conflict of interest was reported by the authors.