 High-order and energy-preserving relaxed implicit–explicit Runge–Kutta methods for Hamiltonian PDEsLei Cui, Qiong-Ao Huang and Gengen Zhang Mathematics and Computers in Simulation (MATCOM), 2026, vol. 241, issue PB, 205-224 Abstract: This work presents a mathematical framework to develop energy-preserving, high-order linearly implicit Runge–Kutta (RK) methods for general Hamiltonian PDEs. This reformulation results in a two-stage second-order IMEX-RK method that is unconditionally energy-stable, with its diagonally implicit part satisfying the symplectic condition. In contrast, the search for a third-order IMEX-RK scheme that similarly guarantees unconditional energy-stable has been unsuccessful. To achieve a higher-order energy-preserving scheme, we incorporate a relaxation factor into the conventional IMEX-RK method, leading to the development of a class of high-order relaxed IMEX-RK (RIMEX-RK) methods. A rigorous theoretical analysis demonstrates the derived methods’ energy stability and error convergence. Key advantages of the RIMEX-RK methods include their one-step nature, high-order accuracy, energy preservation, and ease of implementation. Extensive numerical experiments demonstrate the framework’s superior performance. Keywords: Energy conservation; Implicit–explicit Runge–Kutta methods; Relaxation technique; Hamiltonian PDEs (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:241:y:2026:i:pb:p:205-224 DOI: 10.1016/j.matcom.2025.10.012 Access Statistics for this article Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier |
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