Numerical quadrature methods for integrals of singular periodic functions and their application to singular and weakly singular integral equations
Abstract
High accuracy numerical quadrature methods for integrals of singular periodic functions are proposed. These methods are based on the appropriate EulerMaclaurin expansions of trapezoidal rule approximations and their extrapolations. They are used to obtain accurate quadrature methods for the solution of singular and weakly singular Fredholm integral equations. Such periodic equations are used in the solution of planar elliptic boundary value problems, elasticity, potential theory, conformal mapping, boundary element methods, free surface flows, etc. The use of the quadrature methods is demonstrated with numerical examples.
 Publication:

National Aeronautics and Space Administration Report
 Pub Date:
 July 1986
 Bibcode:
 1986nasa.reptV....S
 Keywords:

 Fredholm Equations;
 Numerical Analysis;
 Periodic Functions;
 Quadratures;
 Singular Integral Equations;
 Boundary Element Method;
 Boundary Value Problems;
 Conformal Mapping;
 Elastic Properties;
 Fluid Mechanics and Heat Transfer