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arXiv · 2403.08253

Explicit radial basis function Runge-Kutta methods

Jiaxi Gu·Xinjuan Chen·Jae-Hun Jung
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Abstract

The aim of this paper is to design the explicit radial basis function (RBF) Runge-Kutta methods for the initial value problem. We construct the two-, three- and four-stage RBF Runge-Kutta methods based on the Gaussian RBF Euler method with the shape parameter, where the analysis of the local truncation error shows that the s-stage RBF Runge-Kutta method could formally achieve order s+1. The proof for the convergence of those RBF Runge-Kutta methods follows. We then plot the stability region of each RBF Runge-Kutta method proposed and compare with the one of the correspondent Runge-Kutta method. Numerical experiments are provided to exhibit the improved behavior of the RBF Runge-Kutta methods over the standard ones.

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Jiaxi Gu, Xinjuan Chen, Jae-Hun Jung. 2024-03-13. Explicit radial basis function Runge-Kutta methods. https://arxiv.org/abs/2403.08253

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