Numerical solutions of second-order matrix models using cubic-matrix splines

Many studies of mechanical systems in engineering are based on second-order matrix models. This work discusses the second-order generalization of previous research on matrix differential equations dealing with the construction of approximate solutions for the initial problem Y″(x)=f(x,Y(x),Y′(x))Y″(x)=f(x,Y(x),Y′(x)) using matrix-cubic splines without any dimensional increase. An estimation of the approximation error, the corresponding algorithm of our approach and some illustrative examples are presented.