On some discretization methods for solving a linear matrix ordinary differential equation

摘要

In this paper, some discretization methods are considered for solving a linear matrix ordinary differential equation. Discussion is focused on a family of one step methods which include Euler, backward Euler, and Crank–Nicolson schemes as special cases, as well as the Runge–Kutta methods. As an illustration, detailed convergence and error analysis are given for the family of one step methods. Some numerical examples are provided to show the good performance of the methods.