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Adaptive time-stepping and computational stability. (English) Zbl 1077.65086
Summary: We investigate the effects of adaptive time-stepping and other algorithmic strategies on the computational stability of ordinary differential equation codes. We show that carefully designed adaptive algorithms have a most significant impact on computational stability and reliability. A series of computational experiments with the standard implementation of DASSL and a modified version, including stepsize control based on digital filters, is used to demonstrate that relatively small algorithmic changes are able to extract a vastly better computational stability at no extra expense. The inherent performance and stability of DASSL are therefore much greater than the standard implementation seems to suggest.

MSC:
65L20 Stability and convergence of numerical methods for ordinary differential equations
65L05 Numerical methods for initial value problems involving ordinary differential equations
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
65L80 Numerical methods for differential-algebraic equations
65L50 Mesh generation, refinement, and adaptive methods for ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
34A09 Implicit ordinary differential equations, differential-algebraic equations
Software:
RODAS; DASSL
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