Numerical solution of coupled 1D Burgers' equation by Non-Uniform Algebraic-Hyperbolic B-spline Differential Quadrature Method

Abstract

Present paper deals with the numerical solution of coupled 1D Burgers’ equation by implementing the Non-Uniform Algebraic Hyperbolic (NUAH) B-spline Differential Quadrature Method. In the present paper, the spatial variable discretization is done using NUAH B-spline, and the obtained system of ODE is dealt with using the SSP-RK43 scheme. To get the improvised results, the concept of modified cubic NUAH B-spline is incorporated. To test the effectiveness and accuracy of the proposed scheme, numerical examples are discussed. Stability analysis of the proposed scheme is investigated by the matrix stability analysis method. The present regime is worthwhile to deal with some complex natured PDEs, where finding the analytical solution is cumbersome.

Graphical Abstract

Keywords:

• Differential quadrature method
• coupled 1D Burgers’ equation
• Non-Uniform Algebraic Hyperbolic B-spline
• SSP-RK 43 scheme
• matrix stability analysis method

Conflict of Interest

Authors have no conflict of interest.