Numerical solution of Burgers’ equation with modified cubic B-spline differential quadrature method

Abstract

In this paper, a new numerical method, “modified cubic-B-spline differential quadrature method (MCB-DQM)” is proposed to find the approximate solution of the Burgers’ equation. The modified cubic-B-spline basis functions are used in differential quadrature to determine the weighting coefficients. The MCB-DQM is used in space, and the optimal four-stage, order three strong stability-preserving time-stepping Runge–Kutta (SSP-RK43) scheme is used in time for solving the resulting system of ordinary differential equations. To check the efficiency and accuracy of the method, four examples of Burgers’ equation are included with their numerical solutions, L2 and L∞ errors and comparisons are done with the results given in the literature. The proposed method produces better results as compared to the results obtained by almost all the schemes available in the literature, and approaching to the exact solutions. The presented method is seen to be easy, powerful, efficient and economical to implement as compared to the existing techniques for finding the numerical solutions for various kinds of linear/nonlinear physical models.