Proc. Japan Acad. Ser. A Math. Sci. 87 (7), 109-113, (July 2011) DOI: 10.3792/pjaa.87.109
KEYWORDS: Numerical analysis for partial differential equations, finite difference scheme, Cauchy-Kowalevskaya’s theorem, Ill-posed problems, multiple-precision arithmetic, 65M12, 65J10, 35A10
We show convergence of a finite difference scheme to solve the abstract Cauchy problem on a scale of Banach spaces which includes that for Kowalevskaya’s system. We show convergence of consistent difference schemes even for unstable cases.