The generalized Burger’s–Huxley and Burger’s–Fisher equations are solved by fully different numerical scheme. The equations are discretized in time by a new linear approximation scheme and in space by 2N order compact finite difference scheme, after that a collocation
method is applied. Also, the two-dimensional unsteady Burger’s equation is described by our proposed scheme. Numerical experiments and numerical comparisons are presented to show the efficiency and the accuracy of the proposed scheme.