Approximate Solution of a Model Describing Biological Species Living Together by Taylor Collocation Method

In this paper, a numerical method is presented to obtain approximate solutions for the system of nonlinear delay integro-differential equations derived from considering biological species living together. This method is essentially based on the truncated Taylor series and its matrix representations with collocation points. Also, to illustrate the pertinent features of the method examples are presented and results are compared to the Adomian decomposition method, the variational iteration method, pseudospectral Legendre method. All numerical computations have been performed on the computer algebraic system Maple 15

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