An Error Estimation Technique for the Solution of Ordinary Differential Equations in Chebyshev Series

Most numerical methods for producing approximate Chebyshev series solutions to ordinary differential equations lead to a system of algebraic equations for the coefficients, while the truncation error (or a first order approximation to it for non-linear equations) can be formulated as an infinite series. By solving the algebraic system with additional right-hand sides and by extrapolating the size of the exact coefficients from the computed ones, the first few terms in the error expansion result, giving an accurate error estimate varying with the independent variable unless the series is slowly convergent. The technique is illustrated by numerical examples.