Approximating and computing nonlinear matrix differential models

Differential matrix models are an essential ingredient of many important scientific and engineering applications. In this work, we propose a procedure to represent the solutions of first-order matrix differential equations Y′(x)=f(x,Y(x))Y′(x)=f(x,Y(x)) with approximate matrix splines. For illustration of the method, we choose one scalar example, a simple vector model, and finally a Sylvester matrix differential equation as a test.