A Numerical approximation of two- dimensional non-linear coupled Burgers equation by using cubic Hyperbolic B-spline differential quadrature method

Abstract

Present paper deals with the numerical solution of coupled 2D non-linear Burgers’ equation by implementing the notion of modified cubic Hyperbolic B-spline based Differential quadrature method. Feasibility and accuracy of proposed scheme is checked by using $L_2$ and $L_\infty$ error norms. Comparison of errors is shown for the mentioned examples. Reduced set of ordinary differential equations is tackled by using SSP-RK43 scheme. Stability of the proposed scheme is checked by using the Matrix stability analysis method. It is noticed that proposed numerical scheme produced the results with accuracy and it is quite easy to implement.