A novel approach for numerical computation of Burgers’ equation in (1 + 1) and (2 + 1) dimensions

Abstract

This paper proposes a new scheme termed as modified extended cubic B-Spline differential quadrature (mECDQ) method for time dependent partial differential equations. Specially, the numerical computation of the Burgers’ equation is obtained using mECDQ method. First of all the modified extended cubic B-splines are used as a set of basis function in DQ to evaluate the weighting coefficients. The mECDQ method converts the initial boundary value system of Burgers’ equation into a initial value system of ordinary differential equations (ODEs). The resulting system is solved by using an optimal five stage four order strong stability preserving Runge–Kutta method (SSP-RK54). The accuracy and efficiency of the method is illustrated by considering five test problems. The proposed results are compared with the exact solutions in terms of L2 and L∞ error norms and the existing results. The mECDQ scheme produces better results than the results due to almost all the existing schemes. The stability analysis of the scheme is also carried out using the matrix stability analysis method for various grid points. This shows that mECDQ scheme is conditionally stable.