A hybrid numerical technique for the solution of a class of implicit matrix differential equation

This paper is concerned with the numerical solution of an implicit matrix differential system of the form (YY)-Y-T - F(t, Y) = 0, where Y(t) is a n x n real matrix which may converge to a singular matrix. We propose a hybrid numerical technique based on an implicit second order Runge Kutta scheme which derives a particular algebraic Riccati equation and via its solution approximates the solutions of the differential problem at hand. Numerical examples demonstrating the behavior of the proposed approach are also reported.