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<p>Singly-TASE operators for the numerical solution of stiff differential equations were proposed by Calvo et al. in J.Sci. Comput. 2023 to reduce the computational cost of Runge–Kutta-TASE (RKTASE) methods when the involved linear systems are solved by some <i>LU</i> factorization. In this paper we propose a modification of these methods to improve the efficiency by considering different TASE operators for each stage of the Runge–Kutta. We prove that the resulting RKTASE methods are equivalent to <i>W</i>-methods (Steihaug and Wolfbrandt, Mathematics of Computation,1979) and this allows us to obtain the order conditions of the proposed Modified Singly-RKTASE (MSRKTASE) methods through the theory developed for the <i>W</i>-methods. We construct new MSRKTASE methods of order two and three and demonstrate their effectiveness through numerical experiments on both linear and nonlinear stiff systems. The results show that the MSRKTASE schemes significantly enhance efficiency and accuracy compared to previous Singly-RKTASE (SRKTASE) schemes.</p>

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Modified Singly-Runge–Kutta-TASE Methods for the Numerical Solution of Stiff Differential Equations

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年2月12日

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  • M. Calvo,
  • J. I. Montijano,
  • L. Rández

摘要

Singly-TASE operators for the numerical solution of stiff differential equations were proposed by Calvo et al. in J.Sci. Comput. 2023 to reduce the computational cost of Runge–Kutta-TASE (RKTASE) methods when the involved linear systems are solved by some LU factorization. In this paper we propose a modification of these methods to improve the efficiency by considering different TASE operators for each stage of the Runge–Kutta. We prove that the resulting RKTASE methods are equivalent to W-methods (Steihaug and Wolfbrandt, Mathematics of Computation,1979) and this allows us to obtain the order conditions of the proposed Modified Singly-RKTASE (MSRKTASE) methods through the theory developed for the W-methods. We construct new MSRKTASE methods of order two and three and demonstrate their effectiveness through numerical experiments on both linear and nonlinear stiff systems. The results show that the MSRKTASE schemes significantly enhance efficiency and accuracy compared to previous Singly-RKTASE (SRKTASE) schemes.