An extrapolation procedure for the evaluation of singular integrals

Abstract

An extrapolation procedure for the evaluation of finite range singular integrals is suggested which is based on the application of the e-algorithm to accelerate sequences of quadrature approximations. These sequences are produced by integrating over increasingly small sub-intervals using the powerful pseudo-Gaussian quadrature formulae of Patterson. Extensive numerical tests are carried out on a large number of test integrals and critical comparisons made with existing methods.

Keywords:

• Singular integrands
• non-uniform sub-division
• Patterson quadrature
• ε-algorithm

C.R. Categories::

• 5.16