an:00222310
Zbl 0772.65054
El-Daou, M. K.; Ortiz, E. L.
Error analysis of the Tau method: Dependence of the error on the degree and on the length of the interval of approximation
EN
Comput. Math. Appl. 25, No. 7, 33-45 (1993).
00012620
1993
j
65L70 65L10 65L05 34A34 34B15
error analysis; Tau method; rate of convergence
For the Tau method it is known that the norm of the error function and the sum of the absolute values of the Tau method parameters have the same rate of convergence. In this paper the authors investigate the speed of convergence of the approximation error by concentrating on the behaviour of these parameters.
Basic results are: the parameters decay exponentially in terms of \(n\), for \(n\) fixed parameters decay as \((h/2)^ n\) where \(h\) is the length of the interval on which the approximation is sought. Two examples from initial and boundary value problems for ordinary differential equations are given.
Z.Schneider (Bratislava)