A new technique for numerical solution of 1D and 2D non-linear coupled Burgers’ equations by using cubic Uniform Algebraic Trigonometric (UAT) tension B-spline based differential quadrature method

Abstract

In present paper, a new technique is developed named Uniform Algebraic Trigonometric (UAT) tension B-spline based DQM, for the better numerical approximation of coupled 1D and coupled 2D Burgers’ equation. The formula of UAT tension B-spline of order 4 is developed in this paper, by using above-mentioned basis function. Strong stability preserving SSP-RK 43 method is implemented to solve obtained ordinary differential equations. To check the effectiveness and accuracy of the proposed scheme, L2 and L∞error norms are used. Four numerical experiments are discussed to put light upon applicability of scheme. By means of tables and figures, results obtained are given. Obtained results are in a good agreement with existing ones. Stability of proposed scheme is also checked by implementing the Matrix stability analysis method. This novel scheme will surely open some new dimensions in the field of numerical approximation, for other researchers in their future work.

Keywords

• Differential quadrature method
• Coupled 1D and coupled 2D Burgers’ equation
• Uniform Algebraic Trigonometric (UAT) tension B-spline
• Strong stability preserving Runge-Kutta – 43 method
• Error norms
• Matrix stability analysis method.