Parallelism in the Numerical Integration of Initial Value Problems.

Numerical Integration of Initial Value Problems in Ordinary Differential Equations

The approach described in the first part of this paper is extended to include diagonally implicit Runge-Kutta (DIRK) formulae. The algorithms developed are suitable for the numerical integration of stiff differential systems, and their efficiency is illustrated by means of some numerical examples.

Optimal Stability Polynomials for Numerical Integration of Initial Value Problems

Trigonometrically fitted two-step obrechkoff methods for the numerical solution of periodic initial value problems

In this paper, we present a new two-step trigonometrically fitted symmetric Obrechkoff method. The method is based on the symmetric two-step Obrechkoff method, with eighth algebraic order, high phase-lag order and is constructed to solve IVPs with periodic solutions such as orbital problems. We compare the new method to some recently constructed optimized methods from the literature. The numeri...

Stiffness in numerical initial-value problems

This paper reviews various aspects of stiffness in the numerical solution of initial-value problems for systems of ordinary differential equations. In the literature on numerical methods for solving initial value problems the term "stiff" has been used by various authors with quite different meanings, which often causes confusion. This paper attempts to clear up this confusion by reviewing some...

Block Runge-Kutta Methods for the Numerical Integration of Initial Value Problems in Ordinary Differential Equations

Block Runge-Kutta formulae suitable for the approximate numerical integration of initial value problems for first order systems of ordinary differential equations are derived. Considered in detail are the problems of varying both order and stepsize automatically. This leads to a class of variable order block explicit Runge-Kutta formulae for the integration of nonstiff problems and a class of v...