Abstract
In this paper, an implicit finite-difference method is proposed for the numerical solutions of one-dimensional coupled nonlinear Burgers' equations on the uniform grid. The proposed Crank–Nicolson scheme forms a system of nonlinear difference equations which has to be solved at each iteration. The nonlinear assembled system of equations has been linearized by applying Newton's iteration method. The obtained linear system has been solved by using Gauss elimination with partial pivoting method. Three numerical examples have been given in order to demonstrate the accuracy and efficiency of the proposed scheme. Computed results have been compared well with the analytical solutions and those already available in the literature via the error norms.
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