Robust Exponential Runge-Kutta Embedded Pairs

Thoma Zoto; John C. Bowman

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arXiv · 2303.12139

Robust Exponential Runge-Kutta Embedded Pairs

Thoma Zoto·John C. Bowman

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Abstract

Exponential integrators are explicit methods for solving ordinary differential equations that treat linear behaviour exactly. The stiff-order conditions for exponential integrators derived in a Banach space framework by Hochbruck and Ostermann are solved symbolically by expressing the Runge--Kutta weights as unknown linear combinations of phi functions. Of particular interest are embedded exponential pairs that efficiently generate both a high- and low-order estimate, allowing for dynamic adjustment of the time step. A key requirement is that the pair be robust: if the nonlinear source function has nonzero total time derivatives, the order of the low-order estimate should never exceed its design value. Robust exponential Runge--Kutta (3,2) and (4,3) embedded pairs that are well-suited to initial value problems with a dominant linearity are constructed.

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Thoma Zoto, John C. Bowman. 2023-03-21. Robust Exponential Runge-Kutta Embedded Pairs. https://arxiv.org/abs/2303.12139

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