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Spline-oriented inter/extrapolation-based multirate schemes of higher order (2207.02732v1)
Published 6 Jul 2022 in math.NA and cs.NA
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.