Solving second-order matrix differential equations with regular singular points avoiding the increase of the problem dimension

摘要

In this paper we propose a method for solving second order matrix differential systems of the form t2X”+tA(t)X′+B(t)X=0, where A and B are analytic matrix functions in a neighborhood of t = 0. Series solutions of the problem are constructed without increasing the problem dimension. By introducing the concept of a fundamental set of solutions of the above equation, an analogous result to the Frobenius theorem to solve the corresponding scalar equation is presented.