Exponential decay of errors of a fundamental solution method applied to a reduced wave problem in the exterior region of a disc

This paper concerns a fundamental solution method (FSM, in abbreviation) applied to a reduced wave problem in the exterior region of a disc. The convergent rate of approximate solutions to the exact one is proven to be asymptotically exponentially decreasing with respect to the number NN of collocation points employed in an approximate problem. Using obtained FSM solutions we add two numerical tests: numerical estimate of errors including cases of high wave numbers; and visualization of total waves appeared in the scattering phenomena around a circular obstacle in the cases of κ=50κ=50 and κ=100κ=100, where κκ is a normalized wave number, defined through κ=κ= length of wave number vector ×× radius of the disc. In the second test, the total waves almost vanish behind the disc, seemingly corresponding to the phenomenon of shadowing in the classical literature of physics.