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.
"Convergence of a semi-discrete finite difference scheme applied to the abstract Cauchy problem on a scale of Banach spaces." Proc. Japan Acad. Ser. A Math. Sci. 87 (7) 109 - 113, July 2011. https://doi.org/10.3792/pjaa.87.109