High-precision numerical computation of integral equations of the first kind(Scientific Computation and Numerical Analysis; Basics and Applications of Multiprecision Scientific Computation, <Special Issue>Joint Symposium of JSIAM Activity Groups 2005)

Abstract

A new method for the direct numerical computation of integral equations of the first kind, of which the integral kernels are analytic, is proposed. The basic idea of the method is based on combination of the spectral collocation method and the multiple precision computation. It gives good numerical results for the equations as far as we don't admit observation errors in the given inhomogeneous terms, and the results implies possibility of numerical analytic continuation on the multiple precision arithmetic. A new accurate rule for numerical integration is also introduced.