A Fundamental Solution Method with Multiple-precision Computation Applied to Reduced Wave Neumann Problems in the Exterior Region of a Disc(Scientific Computation and Numerical Analysis; Basics and Applications of Multiprecision Scientific Computation, <Special Issue>Joint Symposium of JSIAM Activity Groups 2005)

Abstract

This paper concerns a fundamental solution method applied to Neumann boundary value problems of two dimensional reduced wave equations in the exterior region of a disc. A criterion for the unique solvability of the derived approximate problems and an error estimation for their solutions are obtained. The obtained decay rate of error is asymptotically exponential. Some results of our numerical experiments are also reported, which support the effectiveness of multiple-precision computation applied to our schemes.