Multi-step Residual Power Series Method for Solving Stiff Systems

Authors

  • M. Al Zurayqat
  • S. Hasan Department of Applied Science, Ajloun College, Al-Balqa Applied University, Ajoun 26816, Jordan {2} Jadara Research Center, Jadara University, Irbid 21110, Jordan https://orcid.org/0000-0002-3601-5568

DOI:

https://doi.org/10.29020/nybg.ejpam.v17i4.5437

Keywords:

Multi-step method, Residual power series method, Stiff system , numerical solution , Caputo Fractional derivatives

Abstract

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.

Author Biography

  • S. Hasan, Department of Applied Science, Ajloun College, Al-Balqa Applied University, Ajoun 26816, Jordan {2} Jadara Research Center, Jadara University, Irbid 21110, Jordan

    Assistant Professor at the Department of Applied Science, Ajloun College, Al-Balqa Applied University, Ajoun 26816, Jordan

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Published

2024-10-31

Issue

Section

Nonlinear Analysis

How to Cite

Multi-step Residual Power Series Method for Solving Stiff Systems. (2024). European Journal of Pure and Applied Mathematics, 17(4), 2939-2961. https://doi.org/10.29020/nybg.ejpam.v17i4.5437