On the numerical solution of stiff systems

In this paper, we use power series method to solve stiff ordinary differential equations of the first order and an ordinary differential equation of any order by converting it into a system of differential of the order one. Theoretical considerations has been discussed and some examples were presented to show the ability of the method for linear and nonlinear systems of differential equations. We use MAPLE computer algebra systems for numerical calculations [G. Frank, MAPLE V, CRC Press Inc., Florida, 1996].