Efficient high-order two-derivative DIRK methods with optimized phase errors

Fuente: arXiv
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Main Authors: Ehigie, Julius, Luan, Vu Thai
Format: Preprint
Published: 2025
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author Ehigie, Julius
Luan, Vu Thai
author_facet Ehigie, Julius
Luan, Vu Thai
contents This work constructs and analyzes new efficient high-order two-derivative diagonally implicit Runge--Kutta (TDDIRK) schemes with optimized phase errors. Specifically, we present a convergence result for TDDIRK methods and investigate their optimized phase errors and linear stability analysis. Based on these, we derive new families of 2-stage fourth-order, 2-stage fifth-order, and 3-stage fifth-order TDDIRK schemes. Finally, we provide numerical experiments at both the ODE and PDE levels to demonstrate the accuracy and efficiency of these new schemes compared to known DIRK schemes in the literature.
format Preprint
id arxiv_https___arxiv_org_abs_2512_15227
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Efficient high-order two-derivative DIRK methods with optimized phase errors
Ehigie, Julius
Luan, Vu Thai
Numerical Analysis
65L05, 65M20
This work constructs and analyzes new efficient high-order two-derivative diagonally implicit Runge--Kutta (TDDIRK) schemes with optimized phase errors. Specifically, we present a convergence result for TDDIRK methods and investigate their optimized phase errors and linear stability analysis. Based on these, we derive new families of 2-stage fourth-order, 2-stage fifth-order, and 3-stage fifth-order TDDIRK schemes. Finally, we provide numerical experiments at both the ODE and PDE levels to demonstrate the accuracy and efficiency of these new schemes compared to known DIRK schemes in the literature.
title Efficient high-order two-derivative DIRK methods with optimized phase errors
topic Numerical Analysis
65L05, 65M20
url https://arxiv.org/abs/2512.15227