The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods
The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Estimating local truncation errors for Runge-Kutta methods
Journal of Computational and Applied Mathematics - Special issue on numerical methods for ordinary differential equations
On the construction of error estimators for implicit Runge-Kutta methods
Journal of Computational and Applied Mathematics
Stiff differential equations solved by Radau methods
Proceedings of the on Numerical methods for differential equations
Multi-step zero approximations for stepsize control
Applied Numerical Mathematics - Auckl numerical ordinary differential equations (ANODE 98 workshop)
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This paper is concerned with local error estimation in the numerical integration of stiff systems of ordinary differential equations by means of Runge--Kutta methods. With implicit Runge--Kutta methods it is often difficult to embed a local error estimate with the appropriate order and stability properties. In this paper local error estimation based on the information from the last two integration steps (that are supposed to have the same steplength) is proposed. It is shown that this technique, applied to Radau IIA methods, lets us get estimators with proper order and stability properties. Numerical examples showing that the proposed estimate improves the efficiency of the integration codes are presented.