Frobenius-Chebyshev polynomial approximations with a priori error bounds for nonlinear initial value differential problems

In this paper, we present a method for approximating the solution of initial value ordinary differential equations with a priori error bounds. The method is based on a Chebyshev perturbation of the original differential equation together with the Frobenius method for solving the equation. Chebyshev polynomials in two variables are developed. Numerical results are presented.