Optimality of an error estimate of a one-step numerical integration method for certain initial value problems

Abstract

In a recent paper, an error estimate of a one-step numerical method, originated from the Lanczos tau method, for initial value problems for first order linear ordinary differential equations with polynomial coefficients, was obtained, based on the error of the Lanczos econo-mization process. Numerical results then revealed that the estimate gives, correctly, the order of the tau approximant being sought. In the present paper we further establish that the error estimate is optimum with respect to the integration of the error equation. Numerical examples are included for completeness.

Keywords:

• Error
• error estimate
• error problem
• integrated error equation
• one-step method
• canonical polynomials
• Chebyshev polynomials
• initial value problems

C.R. Categories:

• G.1.7