A new high-accuracy method based on off-step cubic polynomial approximations for the solution of coupled Burgers’ equations and Burgers–Huxley equation

Using two off-step points and a central point, we discuss a new two-time-level implicit method of order three based on polynomial cubic spline approximations for the solution of the system of 1D nonlinear parabolic equations on a quasi-variable mesh. The proposed method is derived directly from the consistency condition. The stability analysis for a model problem is discussed. The proposed method is tested to solve the coupled Burgers’ equations and Burgers–Huxley equation to demonstrate the utility of the method. We show that the proposed method enables us to obtain the high-accurate numerical solution for high Reynolds number.