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(k2+k2h2+h2) to O(k2+k2h2+h4) 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.