Numerical solutions of second order matrix differential equations using basis splines

Abstract

This paper aims to present a general framework of the cubic, quintic and septic B-splines functions to develop a numerical method for obtaining approximation solution numerical solution of the matrix differential equations of second order with boundary conditions. Numerical examples are included to illustrate the practical implementation of the proposed method.  The results reveal that the proposed approach is very effective, convenient and quite accurate to such considered problems compared with cubic splines with constant term method.