Spline-oriented inter/extrapolation-based multirate schemes of higher order

TL;DR

This paper introduces a new class of multirate integration schemes using clamped cubic splines, achieving up to 4th order convergence for systems with components evolving at different rates.

Contribution

It develops a novel subclass of inter/extrapolation-based multirate schemes employing cubic splines, extending the order of accuracy to four.

Findings

Achieves 4th order convergence in numerical experiments

Demonstrates effectiveness on a multi-mass oscillator model

Extends multirate schemes to higher order accuracy

Abstract

Multirate integration uses different time step sizes for different components of the solution based on the respective transient behavior. For inter/extrapolation-based multirate schemes, we construct a new subclass of schemes by using clamped cubic splines to obtain multirate schemes up to order 4. Numerical results for a $n$-mass-oscillator demonstrate that 4th order of convergence can be achieved for this class of schemes.