Untitled Page 1 Page 2 Springer Series in 8 Computational Mathematics Editorial Board R.
Bank RL Graham J. Stoer R. Varga H. Yserentant Page 3 E. Hairer SP Nørsett G. Wanner …

The main purpose of the book is to introduce the readers to the numerical integration of the
Cauchy problem for delay differential equations (DDEs). Peculiarities and differences that …

Abstract Explicit Runge–Kutta pairs are known to provide efficient solutions to initial value
differential equations with inexpensive derivative evaluations. Two criteria for selection are …

Explicit Runge--Kutta (RK) methods in the form of pairs of orders p (p-1) provide an attractive
means for the solution of initial value problems of first-order differential equations. Most …

We compare the three main types of high-order one-step initial value solvers: extrapolation,
spectral deferred correction, and embedded Runge–Kutta pairs. We consider orders four …

We present two pairs of embedded Runge‐Kutta type methods for direct solution of fourth‐
order ordinary differential equations (ODEs) of the form y (iv)= f (x, y) denoted as RKFD …

Improvements over a Runge-Kutta pair of orders six and five are presented in this paper.
Methods with minimised truncation errors, phase-lag errors, dissipation errors, and with …

A tenth-order explicit Runge-Kutta method with embedded results of order eight is exhibited.
The difference between the results of orders eight and ten can be used to estimate the local …

In this paper we consider ordinary differential equations with a known Lyapunov function.
We study the use of Runge–Kutta methods provided with a dense output and a projection …

A wide range of quantum systems are time-invariant and the corresponding dynamics is
dictated by linear differential equations with constant coefficients. Although simple in …