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

Explicit Stabilized Runge-Kutta Methods

2-stage explicit total variation diminishing preserving Runge-Kutta methods

In this paper, we investigate the total variation diminishing property for a class of 2-stage explicit Rung-Kutta methods of order two (RK2) when applied to the numerical solution of special nonlinear initial value problems (IVPs) for (ODEs). Schemes preserving the essential physical property of diminishing total variation are of great importance in practice. Such schemes are free of spurious o...