Numerical approximation of coupled 2D Burger's equation by employing non-uniform algebraic hyperbolic (NUAH) B-spline based differential quadrature method

Abstract

In this work, a numerical regime based upon the Non-uniform algebraic hyperbolic B-spline is developed with the aid of differential quadrature method named “NUAH B-spline Differential quadrature methodâ€, in order to fetch the numerical approximation of non-linear coupled 2d Burgers’ equation. In first step, the spatial discretization is mentioned by using the NUAH B-spline of order 4, for improvised results, modified formulae are implemented. In second step, the reduced system of ordinary differential equations is dealt with the strong stability preserving Runge-Kutta 43 method (SSP-RK43 method). The proposed regime is analyzed for stability also. Finally, the effectiveness and adaptability of the proposed regime is confirmed with the aid of numerical experiments and fetched results are compared with the existing outcomes in literature. It is observed that the present scheme is unconditionally stable, by implementing the concept of matrix stability analysis method. it is found that present regime is easy to implement and produces the accurate results.