In the present paper, a numerical method is proposed for the numerical solution of a coupled system of Burgers’ equation by using the quintic B-spline collocation scheme on the uniform mesh points. The method is shown to be unconditionally stable using von Neumann technique. To test accuracy the error norms  are computed and give some examples to illustrate the sufficiency of the method for solving such nonlinear partial differential equations. Computed results are depicted graphically and are compared with those already available in the literature.

collocation method, quintic B-splines method, coupled Burgers’ equations.