Numerical solution of integral equations with logarithmic-, Cauchy- and Hadamard-type singularities

Abstract

This study presents an extension of the piecewise quadratic polynomial technique to solve singular integral equations with logarithmic- and Hadamard-type singularities. For completeness and continuity, the evaluation of the weights for logarithmic-, Cauchy- and Hadamard-type singularities are given explicitly. Numerical results concerning logarithmic- and Hadamard-type singular integral equations are compared with the known solutions. The solution of Cauchy-type singular integral equations was discussed in detail in a previous study by Miller and Keer. © 1998 John Wiley & Sons, Ltd.