Initial value problems: Numerical methods and mathematics
The author summarizes his research on Runge-Kutta (RK) and related general linear methods for approximation to the solution of ordinary differential equations. An explanation is given of the way to apply a general series, now called a B-series (Butcher series), to the study of particular RK algorithms. A proof is given of the A-stability of implicit RK algorithms. Criteria for stability and consistency of general linear algorithms are presented. Finally a criterion is given for the stability of a new class of algorithms, called diagonally implicit multistage integration methods (DIMSIM's), developed by the author. Some of these are designed to treat stiff systems by means of parallel computations.
diagonally implicit multistage integration methods
scientific article; zbMATH DE number 699063
scientific article