Explicit general linear methods with inherent Runge–Kutta stability. (English) Zbl 1016.65049

Wright, W. M.

Numer. Algorithms 31, No. 1-4, 381-399 (2002).

The goal of the paper is the construction of a new class of practically useful general linear methods for the numerical solution of non-stiff ordinary differential equations. The methods are generated in a way that guarantees that their stability regions are large (indeed, identical to the stability regions of certain Runge-Kutta methods). The stage order of the new methods is high, thus allowing efficient error estimates and the construction of high order interpolants. The main properties of the rules are described. A section of the paper is devoted to the question of finding the methods explicitly. Some special cases are given in detail. Numerical experiments indicate the quality of the new methods.

Reviewer: Kai Diethelm (Braunschweig)

MSC:

65L06	Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
65L05	Numerical methods for initial value problems involving ordinary differential equations
65L20	Stability and convergence of numerical methods for ordinary differential equations
65L70	Error bounds for numerical methods for ordinary differential equations
34A34	Nonlinear ordinary differential equations and systems

Keywords:

general linear methods; inherent Runge-Kutta stability; Nordsieck form; stability regions; Runge-Kutta methods; error estimates; numerical experiments

Software:

DESIRE; RADAU