This paper gives a modification of a class of stochastic Runge-Kutta methods proposed in a paper by Komori (2007). The slight modification can reduce the computational costs of the methods significantly.

In this paper a domain Ω ⊆ C is a connected open set. We let O Ω denote the algebra of holomorphic functions on Ω. We will use the following notation: D denotes the unit disc in the complex plane. We let D2 D × D denote the bidisc, and D D × D × · · · × D the polydisc in C. The symbol B Bn is the unit ball in C. A domainΩ ⊆ C is said to be Runge if any holomorphic f onΩ is the limit, uniformly ...

We describe the derivation of order conditions, without restrictions on stage order, for general linear methods for ordinary differential equations. This derivation is based on the extension of Albrecht approach proposed in the context of Runge-Kutta and composite and linear cyclic methods. This approach was generalized by Jackiewicz and Tracogna to two-step Runge-Kutta methods, by Jackiewicz a...

_________________________________________________ Vernon W. Ruttan is Regents Professor in the Department of Applied Economics and in the Department of Economics at the University of Minnesota. This paper draws on two earlier papers (Ruttan, 1998; in press). I am indebted to Donald N. Duvick, Nicholas Kalaitzandonakes, John M. Reilly, C. Ford Runge, W. Burt Sundquist, and Paul E. Waggoner for c...

This paper presents a new simple technique to improve the order behaviour of Runge-Kutta methods when applied to index 2 DAEs. It is then shown how this can be incorporated into a more eecient version of the code RADAU5 developed by E. Hairer and G. Wanner.

In this paper we investigate Donder-Weyl (DW) Hamilton-Jacobi equations and establish the connection between DW Hamilton-Jacobi equations and multi-symplectic Hamiltonian systems. Based on the study of DW Hamilton-Jacobi equations, we present the generating functions for multi-symplectic partitioned Runge-Kutta (PRK) methods.

For Hamiltonian systems with non-canonical structure matrix a new class of numerical integrators is proposed. The methods exactly preserve energy, are invariant with respect to linear transformations, and have arbitrarily high order. Those of optimal order also preserve quadratic Casimir functions. The discussion of the order is based on an interpretation as partitioned Runge–Kutta method with ...

The parametric instability arising when ordinary differential equations (ODEs) are numerically integrated with Runge-Kutta-Nyström (RKN) methods with varying step sizes is investigated. Perturbation methods are used to quantify the critical step sizes associated with parametric instability. It is shown that there is no parametric instability for linear constant coefficient ODEs integrated with ...