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

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.


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


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