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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.

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
Full Text: DOI
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