Explicit parallel two-step Runge-Kutta-Nyström 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...

Runge-Kutta-Nyström-type parallel block predictor-corrector methods

This paper describes the construction of block predictor-corrector methods based on Runge-Kutta-Nystrr om correctors. Our approach is to apply the predictor-corrector method not only with stepsize h, but, in addition (and simultaneously) with stepsizes a i h; i = 1; : : :; r. In this way, at each step, a whole block of approximations to the exact solution at oo-step points is computed. In the n...

High Order Explicit Two-Step Runge-Kutta Methods for Parallel Computers

R n , parameters A aij R s , c b R , 1l : 1 1 T and step size hm. F denotes the straightforward extension of f to R . Here, denotes the Kronecker tensor product. Notice that the EPTRK method 2 requires only one sequential function evaluation per step on a parallel computer with s processing elements. Numerical experiments with a variable step size implementation on a shared memory computer have...

Continuous Explicit Runge-Kutta methods