Abstract
A modification of the Lanczos Tau Method for the approximate solution of second-order differential equations with polynomial coefficients was proposed by the author earlier. This modification chooses a minimum perturbation, among all possible, on the right-hand side of the corresponding Volterra integral equation. A Tau Method computational scheme is applied to the approximate solution of a system of differential equations related to the differential equation of hypergeometric type. Various vector perturbations are discussed. Our choice of the perturbation term is a shifted Chebyshev polynomial with a special form of selected transition and normalization. The minimality conditions for the perturbation term are found for one equation. They are sufficiently simple for verification in a number of important cases. Ortiz's recursive approach to the Tau Method is extended to canonical vector-polynomial coefficients, and to the coefficients of the linear combination that generate an approximate solution. The advantages of the proposed approach are shown for modified Bessel functions computation. Seven digit tables of modified Bessel function K 1 2+iβ (x) have been computed and published. The computer programs for the calculations may be found in the State Fund of Algorithms and Programs and in the United Library of Numerical Analysis of the Moscow State University.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.