Nodal Spline Integration Rules for Certain 2-D Cauchy Principal Value Integrals

In this paper we consider integration rules based on products of one-dimensional nodal spline quadratures for the numerical evaluation of 2-D singular integrals defined in the Hadamard finite part sense. We derive convergence results and error bounds. Some numerical tests are also presented.

Keywords:

• Spline Approximation
• Finite-part Integrals
• Cauchy Principal Value
• Quadratures
• Cubatures