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This paper deals with stability in the numerical solution of the prominentHeston partial differential equation from mathematical finance. We study thewell-known central second-order finite difference discretization, which leadsto large semi-discrete systems with non-normal matrices A. By employing thelogarithmic spectral norm we prove practical, rigorous stability bounds. Ourtheoretical stability results are illustrated by ample numerical experiments.

Stability of central finite difference schemes for the Heston PDE