Abstract: The recursive formulation of dynamical and spectral coefficients which appear when solving 

ODE systems numerically via Evolution operator approach [4] is developed for the general nonlinear 

case. These recursions are simplified for linear case. Some results that strengthen the method are 

obtained for the case of a linear systems with a skew-symmetric coefficient matrix. While in the 

symmetric case some functions are defined to compute the integrals in the representation of the spectral 

coefficients. The algorithm of evolution operator approach is modified so that calculations are reduced to 

a minimum. Finally some test problems are solved using this algorithm and encouraging results are 

obtained. 

Key words:Evolution operator, method of moments, dynamical coefficients spectral coefficients.