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.

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