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<p>In this paper, we construct a new canonical midpoint splitting method and analyze its numerical stability and convergence behavior for solving stiff functional differential-algebraic equations. To reduce the computational effort, we decompose the original problem into a nonstiff subproblem and a stiff subproblem, using the generalized explicit midpoint method to solve the nonstiff subproblem and the implicit midpoint method to solve the stiff subproblem. The results show that the proposed method has second-order convergence under certain conditions. Numerical experiments confirm the correctness of the theoretical results, and a comparison with the IMEX midpoint method concludes that our proposed method can improve computational accuracy and computational speed.</p>

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Theoretical Analysis of Canonical Midpoint Splitting Method for Stiff Functional Differential-Algebraic Equations

  • 期刊论文

  • 发表日期：

    2025年4月9日

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  • Haodong Li,
  • Hongliang Liu,
  • Tan Tan,
  • Yilin You,
  • Shoufu Li

摘要

In this paper, we construct a new canonical midpoint splitting method and analyze its numerical stability and convergence behavior for solving stiff functional differential-algebraic equations. To reduce the computational effort, we decompose the original problem into a nonstiff subproblem and a stiff subproblem, using the generalized explicit midpoint method to solve the nonstiff subproblem and the implicit midpoint method to solve the stiff subproblem. The results show that the proposed method has second-order convergence under certain conditions. Numerical experiments confirm the correctness of the theoretical results, and a comparison with the IMEX midpoint method concludes that our proposed method can improve computational accuracy and computational speed.