Numerical solutions of matrix differential models using cubic matrix splines II

This paper presents the non-linear generalization of a previous work on matrix differential models [E. Defez, L. Soler, A. Hervás, C. Santamaría, Numerical solutions of matrix differential models using cubic matrix splines, Comput. Math. Appl. 50 (2005) 693–699]. It focuses on the construction of approximate solutions of first-order matrix differential equations Y′(x)=f(x,Y(x))Y′(x)=f(x,Y(x)) using matrix-cubic splines. An estimation of the approximation error, an algorithm for its implementation and illustrative examples for Sylvester and Riccati matrix differential equations are given.