Numerical indefinite integration of functions with singularities

Numerical indefinite integration of functions with singularities

We derive an indefinite quadrature formula, based on a theorem of Ganelius, for Hp functions, for p > 1, over the interval (−1, 1). The main factor in the error of our indefinite quadrature formula is O(e−π √ ), with 2N nodes and 1 p + 1 q = 1. The convergence rate of our formula is better than that of the Stenger-type formulas by a factor of √ 2 in the constant of the exponential. We conjectur...

Numerical Integration for Multivariable Functions with Point Singularities

We consider the numerical integration of functions with point singularities over a planar wedge S using isoparametric piecewise polynomial interpolation of the function and the wedge. Such integrals often occur in solving boundary integral equations using the collocation method. In order to obtain the same order of convergence as is true with uniform meshes for smooth functions, we introduce an...

On the Complexity of Self-Validating Numerical Integration and Approximation of Functions with Singularities

A Numerical Integration Method by Using Generalized Series of Functions

Subtracting Out Complex Singularities in Numerical Integration

This paper is concerned with the numerical approximation of definite integrals over [—1, 1], in which the function /to be integrated has isolated singularities near [ —1, 1 ]. Complex variable techniques are used to study the effectiveness of the method of subtracting out complex singularities.