Taylor polynomial approach for systems of linear differential equations in normal form and residual error estimation

The purpose of this paper is to give a matrix method based on Taylor polynomials for solving linear differential equations system with variable coefficients in the normal form under the initial conditions by using residual error function. The presented method converts the problem into a system of algebraic equations via the matrix operations and collocation points. In order to demonstrate the accuracy of solution and efficiency of the method, two numerical examples are given with the help of computer programmes written in Maple and Matlab.