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 \(Y^{T}\dot{Y}-F(t,Y)=0\), where Y(t) is a n × 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.

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