A computational approach using modified trigonometric cubic B-spline for numerical solution of Burgers’ equation in one and two dimensions

Abstract

This article aims to obtain the numerical solution of nonlinear Burgers’ equation in one and two dimensions using hybrid trigonometric differential quadrature method. Simulating five different test problems, the obtained results are compared with exact solution as well as the numerical solution obtained by other researchers. The obtained numerical solutions of this equation are found to have a good match with the exact solutions. To demonstrate the applicability and robustness of the proposed scheme the L2 and L∞ norms are computed and the results are presented both numerically and graphically. The stability of the proposed scheme using the matrix method is also discussed in this article. Keywords: SSP-RK 43, Burgers’ equation, Differential quadrature method, Modified trigonometric B-spline, 2000 MSC: 65M06, 35K57