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arXiv · 2404.16665

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

Hana Mizerová·Katarína Tvrdá
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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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Hana Mizerová, Katarína Tvrdá. 2024-04-25. A new way of deriving implicit Runge-Kutta methods based on repeated integrals. https://arxiv.org/abs/2404.16665

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