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

2025/12/17 by Ehigie, Julius, Luan, Vu Thai
Computer Science · Engineering · Mathematics · #65L05 #65M20 #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · doi:10.48550/arxiv.2512.15227

openalex publication_date 2025/12/17 · openalex created_date 2025/12/19 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Exponentially fitted two-derivative DIRK methods for oscillatory differential equations
• Diagonally Implicit Runge–Kutta Methods for Stiff O.D.E.’s

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