Abstract
A class of quadrature formulae is presented applicable to both nonsingular and singular functions, generalizing the classical endpoint corrected trapezoidal quadrature rules. While the latter rules are usually derived by means of the Euler--Maclaurin formula, their generalizations are obtained as solutions of certain systems of linear algebraic equations. A procedure is developed for the construction of very high-order quadrature rules, applicable to functions with a priori specified singularities, and relaxing the requirements on the distribution of nodes. The scheme applies not only to nonsingular functions but also to a wide class of functions with monotonic singularities. Numerical experiments are presented demonstrating the practical usefulness of the new class of quadratures. Tables of quadrature weights are included for singularities of the form $s(x) = |x|^\lambda$ for a variety of values of $\lambda$, and $s(x) = \log{|x|}$.
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.