Splitting-up Technique and Cubic Spline Approximations For Solving Modified Coupled Burgers' Equations

Abstract

In this paper, a finite difference scheme based on the splitting-up technique and cubic spline approximations is
developed for solving modified coupled Burgers' equations. The accuracy and stability of the scheme have been
analyzed. It is found that the scheme is of first-order accuracy in time and second-order accuracy in space direction
and is unconditionally stable. The numerical results are obtained with severe/moderate gradients in the initial and
boundary conditions and the steady state solutions are plotted for different values of given parameters. It is concluded
that the resulting scheme produces satisfactory results, even in the case of very severe gradient in the solution, and is
applicable at both low and high Reynolds numbers. Also, the general nature of the proposed scheme provides a wider
application in the solution of non-linear problems arising in mechanics and other areas