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Error estimates and adaptive time step control for a class of one-step methods for stiff ordinary differential equations. (English) Zbl 0661.65076

A special class of implicit one-step methods obtained by discretizing in time the discontinuous Galerkin method with piecewise polynomials of varying degrees is considered and error estimates for these methods are obtained when solving stiff ordinary differential equations. An algorithm for variable stepsize control is developed based on these error estimates.
Reviewer: K.Burrage

MSC:

65L05 Numerical methods for initial value problems involving ordinary differential equations
65L50 Mesh generation, refinement, and adaptive methods for ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
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