Regularized product intergration for Hadamard finite part integrals
This paper describes a method for the numerical computation of Hadamard finite-part integrals. The formulas developed are based on equally spaced integrand evaluation points. A novel feature of the approach taken in this paper is the use of points outside of the integration region for the construction of finite difference approximations to the integrand derivatives. Linear splines are used in the analysis of the formulas. The analysis allows for the presence of noise and the new formulas are shown to be stable if the stepsize is chosen appropriately. The convergence of the formulas is shown to be independent of the singularity exponent for the finite-part integral. Numerical results are given which demonstrate the effectiveness of the new formulas when they are applied to three example problems.
scientific article; zbMATH DE number 826960