Variable-stepsize explicit two-step Runge-Kutta methods

A Class Of Implicit-Explicit Two-Step Runge-Kutta Methods

This work develops implicit-explicit time integrators based on two-step Runge-Kutta methods. The class of schemes of interest is characterized by linear invariant preservation and high stage orders. Theoretical consistency and stability analyses are performed to reveal the properties of these methods. The new framework offers extreme flexibility in the construction of partitioned integrators, s...

High Order Explicit Two - Step Runge - Kutta

In this paper we study a class of explicit pseudo two-step Runge-Kutta methods (EPTRK methods) with additional weights v. These methods are especially designed for parallel computers. We study s-stage methods with local stage order s and local step order s + 2 and derive a suucient condition for global convergence order s+2 for xed step sizes. Numerical experiments with 4-and 5-stage methods sh...

Continuous Explicit Runge-Kutta methods

Stepsize selection for tolerance proportionality in explicit Runge-Kutta codes

The potential for adaptive explicit Runge–Kutta (ERK) codes to produce global errors that decrease linearly as a function of the error tolerance is studied. It is shown that this desirable property may not hold, in general, if the leading term of the locally computed error estimate passes through zero. However, it is also shown that certain methods are insensitive to a vanishing leading term. M...

Explicit Stabilized Runge-Kutta Methods