ERROR BOUND ON THE SOLUTION OF A LINEAR-DIFFERENTIAL EQUATION IN CHEBYSHEV SERIES

A bound is derived for the norm of the difference between the solution of a linear differential equation with known input, and an approximat e solution obtained by expansion in a Chebyshev series. The approach i s to derive a bound on the difference between two approximate solution s of different order. This bound is obtained in terms of the order of the approximation of lowest degree, the difference in the orders of ap proximation, and certain matrix norms. Extending this expression so th at it is valid for arbitrarily large differences in order yields a nor m bound on the difference between the approximate solution and the exa ct solution. The basic approach can be extended to other orthogonal fu nction sets.