Numerical regime for coupled 2D Burgers’ equation by employing Barycentric Lagrange interpolation differential quadrature method

Abstract

In the present paper, a Barycentric Lagrange interpolation polynomial-based Differential quadrature method is applied to get the numerical solution of non-linear coupled 2D Burgers’ equation. For this process, first of all, the coupled Burgers’ equation is dealt with generalized formula. By using the obtained generalized formula, required weighting coefficients in the differential quadrature method are easily calculated. Afterward, the reduced set of ordinary differential equations is solved by using the SSP-RK43 scheme. To test the efficiency of the newly applied method, the $L_\infty$ error norm has been computed. To test the stability of the proposed method, the Matrix stability analysis method is implemented, which shows that the developed method is unconditionally stable.