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<p>Preserving invariants of differential equations under discretization can be important, e.g., to improve the qualitative and quantitative properties of numerical solutions. Recently, relaxation methods have been proposed as small modifications of standard time integration schemes guaranteeing the correct evolution of functionals of the solution. We investigate how to combine relaxation with error-based step size control for explicit Runge-Kutta methods using the first-same-as-last (FSAL) technique and demonstrate the improved efficiency of our new methods.</p>

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Relaxation Runge-Kutta Methods with First-Same-as-Last Structure

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年12月4日

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  • Sebastian Bleecke,
  • Hendrik Ranocha

摘要

Preserving invariants of differential equations under discretization can be important, e.g., to improve the qualitative and quantitative properties of numerical solutions. Recently, relaxation methods have been proposed as small modifications of standard time integration schemes guaranteeing the correct evolution of functionals of the solution. We investigate how to combine relaxation with error-based step size control for explicit Runge-Kutta methods using the first-same-as-last (FSAL) technique and demonstrate the improved efficiency of our new methods.