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<p>In this paper, exponential Runge–Kutta methods of collocation type (ERKC) which were originally proposed in (Appl Numer Math 53:323–339, 2005) are extended to semilinear parabolic problems with time-dependent delay. Two classes of the ERKC methods are constructed and their convergence properties are analyzed. It is shown that methods with <i>s</i> arbitrary nonconfluent collocation parameters achieve convergence of order <i>s</i>. Provided that the collocation parameters fulfill some additional conditions and the solutions of the problems exhibit sufficient temporal and spatial smoothness, we derive superconvergence results. Finally, some numerical experiments are presented to illustrate our theoretical results.</p>

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Exponential Runge–Kutta methods of collocation type for parabolic equations with time-dependent delay

  • 期刊论文

  • 发表日期：

    2025年12月22日

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  • Qiumei Huang,
  • Alexander Ostermann,
  • Gangfan Zhong

摘要

In this paper, exponential Runge–Kutta methods of collocation type (ERKC) which were originally proposed in (Appl Numer Math 53:323–339, 2005) are extended to semilinear parabolic problems with time-dependent delay. Two classes of the ERKC methods are constructed and their convergence properties are analyzed. It is shown that methods with s arbitrary nonconfluent collocation parameters achieve convergence of order s. Provided that the collocation parameters fulfill some additional conditions and the solutions of the problems exhibit sufficient temporal and spatial smoothness, we derive superconvergence results. Finally, some numerical experiments are presented to illustrate our theoretical results.