Rational Transformations for Evaluating Singular Integrals by the Gauss Quadrature Rule

Abstract

In this work we introduce new rational transformations which are available for numerical evaluation of weakly singular integrals and Cauchy principal value integrals. The proposed rational transformations include parameters playing an important role in accelerating the accuracy of the Gauss quadrature rule used for the singular integrals. Results of some selected numerical examples show the efficiency of the proposed transformation method compared with some existing transformation methods.

Keywords

• rational transformation
• weakly singular integrals
• Cauchy principal value integrals
• Gauss-Legendre quadrature rule