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

Johnson, Claes

SIAM J. Numer. Anal. 25, No. 4, 908-926 (1988).

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

Keywords:

implicit one-step methods; discontinuous Galerkin method; error estimates; stiff ordinary differential equations; variable stepsize control