The decomposition method for solving a second kind fredholm integral equation with a logarithmic kernel

Abstract

In this paper, Adomian's decomposition method is effectively implemented for solving a second kind boundary integral equation with a logarithmic kernel. The solution obtained is in the form of a convergent power series with easily and elegantly computable terms. The technique has been illustrated by some examples arising from the two-dimensional Helmholtz equation with Dirichlet boundary conditions which are of physical interest. Comparing our scheme with existing collocation and iterative quadrature techniques shows that the present approach is highly accurate, converges rapidly and entirely new in implementing Adomian's technique for complex kernel.