Tension spline method for solution of non-linear Fisher equation

Tension spline method is proposed for the non-linear Fisher equation with initial-boundary values. The three time-level implicit method based on the non-polynomial cubic tension spline is developed for the solution of the non-linear reaction-diffusion equation. The method involves the parameters and its order can be increased from O(k(2) + k(2)h(2) + h(2)) to O(k(2) + k(2)h(2) + h(4)) by an appropriate choice of the parameters. The stability of proposed method is analyzed. Finally, numerical results are presented to demonstrate the accuracy and efficiency of this method. (C) 2014 Elsevier Inc. All rights reserved.