Multi-step Residual Power Series Method for Solving Stiff Systems

In this paper, an efficient algorithm based on the residual power series method (RPSM) is presented to solve stiff systems of Caputo fractional order. We apply the RPSM on subintervals to get approximate solutions of these types of systems. The RPSM has advantages that it is suitable to solve linear and nonlinear systems and it gives high accurate results. Modifying this technique to multi-step RPSM considerably reduces the number of arithmetic operations and so reduces the time, especially when dealing with Stiff systems. Several numerical examples are given to show the efficiency, simplicity and the accuracy of the proposed method. Comparing classical RPSM with the new multi-step scheme shows that multi-step RPSM controls the convergence behaviour of the stiff systems. That is, the comparison reveals that MS-FRPSM reduces both absolute and residual errors. More iterations and a smaller step size lead to higher accuracy. Moreover, in MS-FRPSM, the intervals of convergence for the series solution will increase.