Adaptive Time-Stepping and Computational Stability

• We investigate the effects of adaptive time-stepping and other algorithmic strategies on the computational stability of ODE 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.

Subject headings

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Keyword

Computational stability stepsize control adaptive time-stepping PI control digital filters Dassl mathematical software algorithm analysis

Publication and Content Type

art (subject category)

ref (subject category)