ERROR ESTIMATION IN THE NUMERICAL-SOLUTION OF ODE WITH THE TAU METHOD

In this paper, a method is described for obtaining an estimate of the error of the Tau Method for ordinary differential equations; it is based on a modification of the error of Lanczos economization process. Perturbing the integrated error equation does not appear to improve the accuracy of the estimate significantly, while perturbing the homogeneous boundary conditions can lead to an increase in the accuracy of the estimate. In addition, the estimate is represented in terms of Canonical polynomials without any appreciable loss of accuracy. Several examples are given to illustrate the effectiveness of the method, including the incomplete gamma, exponential and Bessel functions.