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Tuesday, August 06

Two Numerical Techniques for Solving Integral Equations with Log-Singular Kernels

Crystal Jernigan, Old Dominion University, Norfolk, VA
Computer Science Research Group Seminar
10:00 AM — 11:00 AM, Research Office Building (ROB), Building 5700, Room L-204
Contact: Cindy Sonewald (sonewaldc@ornl.gov), 865.574.3125

Abstract

Since integral equations with log-singular kernels occur in many branches of physics and engineering there is considerable interest in the development of techniques for their solution. In this talk, two numerical solution techniques are investigated to solve such integral equations; one based on the Galerkin method and the other on the collocation method, both of which use Chebyshev polynomials of the first kind as basis functions. These techniques reduce the problem of solving the singular integral equation to that of solving a system of linear algebraic equations. The use of these methods is then illustrated by solving problems in electrostatics and acoustic scattering, for both real and complex kernels. The accuracy of the techniques turned out to be comparable with the collocation method proving to be slightly more efficient for the problems under consideration.