This centenary history of Runge-Kutta methods contains an appreciation of the early work of
Runge, Heun, Kutta, and Nyström and a survey of some significant developments of these …

Symplecticity is also an important property for exponential Runge–Kutta (ERK) methods in
the sense of structure preservation once the underlying problem is a Hamiltonian system …

Die mathematische Modellierung von physikalisch-technischen sowie auch von
biologischen Prozessen führt häufig auf Anfangswertprobleme für Systeme gewöhnlicher …

Implicit Runge–Kutta methods in time are used in conjunction with the Galerkin method in
space to generate stable and accurate approximations to solutions of the nonlinear (cubic) …

In the last 20 years various stability test problems for DDE solvers have been considered.
These are mainly generalizations of those used for ODEs. For the simplest autonomous …

We consider the initial-value problem for the radially symmetric nonlinear Schrödin\-ger
equation with cubic nonlinearity (NLS) in d= 2 and 3 space dimensions. To approximate …

In this paper we first present stability and error analysis of the fully discrete numerical
schemes for general dissipative systems, in which the implicit Runge–Kutta (IRK) method is …

This paper studies the stability and convergence properties of general Runge-Kutta methods
when they are applied to stiff semilinear systems y′(t)= J (t) y (t)+ g (t, y (t)) with the stiffness …

This paper continues earlier work by the same author concerning the stability and B-
convergence of general linear methods for the numerical solution of nonlinear stiff initial …

We consiuct and analyze itérative methods for the efficient solution of the nonltneai
équations that resuit ftom the application of Implicit Range Kutta methods to the temporal …