Error Estimates and Automatic Time Step Control for Numerical Methods for Stiff Ordinary Differential Equations

摘要

Numerical methods for initial value problems for stiff ordinary differential equations (ODE) are considered. Runge-Kutta methods (RKM) resulting from discretizing in time of a discontinuous Galerkin method (DGM) are studied. A special class of RKM given satisfactory error estimates for monotone ODE, is discussed. This technique is suggested as the basis for rational methods for automatic time step control. This error estimate can be extended to nonlinear ODE when linear autonomous parabolic problems of DGM are analyzed.