Application of Chebyshev series for the integration of ordinary differential equations

摘要

A numerical analytic method is proposed for solving theCauchy problem for normal systems of ordinary differential equations.This method is based on the approximation of the solution and itsderivative by partial sums of shifted Chebyshev series. The coefficientsof the series are determined by with the aid of an iterative processusing Markov’s quadrature formulas. The method yields an analyticalrepresentation of a solution and can be used to solve ordinary differentialequations with a higher accuracy and with a larger discretizationstep compared to the classical methods, such as Runge–Kutta, Adams,and Gear methods.