Approximate Solutions and Error Bounds for Solving Matrix Differential Equations Without Increasing the Dimension of the Problem

Abstract

In this paper we present a method for solving initial value problems related to second order matrix differential equations. This method is based on the existence of a solution of a certain algebraic matrix equation related to the problem, and it avoids the increase of the dimension of the problem for its resolution. Approximate solutions, and their error bounds in terms of error bounds for the approximate solutions of the algebraic problem, are given.