Applied Mathematical Sciences, Vol. 1, 2007, no. 59, 2927 - 2937 Numerical Solution of Second-Order Matrix Differential Models Using Cubic Matrix Splines Abdollah Borhanifar Department of Mathematics University of Mohaghegh Ardabili, Iran borhanifar@uma.ac.ir Reza Abazari Department of Mathematics University of Mohaghegh Ardabili, Iran abazari-r@uma.ac.ir Abstract This paper deals with the construction of approximate solution of second-order matrix linear differential equations using matrix cubic splines. An estimation of the approximation error, an algorithm for its imple- mentation and some illustrative examples are included. Mathematics Subject Classification: 65M10, 65N10, 76D05 Keywords: Second Order Matrix Linear Differential Equation, Cubic Spline 1 Introduction A great variety of phenomena in physics and engineering can be modeled in the form of matrix differential equations. Apart from the problems where the mathematical pattern is written in matrix form, they also appear when special techniques to solve scalar or vectorial problems are used. Examples of such situations are the embedding methods for the study of linear bound- ary value problems [5], shooting method to solve scalar or vectorial problems with boundary value conditions [6], lines method for the numerical integration of partial differential equations [7], or homotopic methods to solve nonlinear systems equations [8].