The solution of nonlinear ordinary differential equations in Chebyshev series

Abstract

The paper describes a simple iterative method for obtaining the solution of an ordinary differential equation in the form of a Chebyshev series. Nonlinear terms which occur in the equation are dealt with by evaluating their components at the Chebyshev points (cos rπ/N), performing the nonlinear equations and then deriving the representative Chebyshev series for the nonlinear term from its values at the Chebyshev points.