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. 2015 Elsevier Inc. All rights reserved.