Hokkaido Mathematical Journal

FUJIWARA Hiroshi, IMAI Hitoshi, TAKEUCHI Toshiki, ISO Yuusuke,

Numerical treatment of analytic continuation with Multiple-precision arithmetic.

Hokkaido Mathematical Journal, 36 (2007) pp.837-847




The aim of this paper is to show numerical treatment of analytic continuation by high-accurate discretization with multiple-precision arithmetic. We deal with the Cauchy problem of the Laplace equation and an integral equation of the first kind with an analytic kernel. We propose high-accurate discretization based on the spectral method, and show some numerical examples with our proposed multiple-precision arithmetic.

MSC(Secondary)47N40, 65J20
Uncontrolled Keywordsanalytic continuation, ill-posed problem, numerical instability, spectral discretization, multiple-precision arithmetic