A new way of deriving implicit Runge-Kutta methods based on repeated integrals

2024/04/25 by Hana Mizerová, Mizerová, Hana, Kataŕına Tvrdá +1
Engineering · Mathematics · Medicine · Physics and Astronomy · #65L04 #65L05 #65L06 #Applied mathematics #Calculus (dental) #Computer science #Differential equation #Electromagnetic Scattering and Analysis #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Mathematical analysis #Mathematics #Medicine #Numerical Analysis (math.NA) #Numerical methods for differential equations #Runge–Kutta methods

paper · pdf · doi:10.48550/arxiv.2404.16665

published in arXiv (Cornell University) (Cornell University)

openalex publication_date 2024/04/25 · openalex created_date 2024/04/27 · openalex updated_date 2026/07/28

Abstract

Runge-Kutta methods have an irreplaceable position among numerical methods designed to solve ordinary differential equations. Especially, implicit ones are suitable for approximating solutions of stiff initial value problems. We propose a new way of deriving coefficients of implicit Runge-Kutta methods. This approach based on repeated integrals yields both new and well-known Butcher's tableaux. We discuss the properties of newly derived methods and compare them with standard collocation implicit Runge-Kutta methods in a series of numerical experiments, including the Prothero-Robinson problem.

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