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Exponential time integration and second-order difference scheme for a generalized Black-Scholes equation. (English) Zbl 1235.91171

Summary: We apply an exponential time integration scheme combined with a central difference scheme on a piecewise uniform mesh with respect to the spatial variable to evaluate a generalized Black-Scholes equation. We show that the scheme is second-order convergent for both time and spatial variables. It is proved that the scheme is unconditionally stable. Numerical results support the theoretical results.

MSC:

91G60 Numerical methods (including Monte Carlo methods)
65N06 Finite difference methods for boundary value problems involving PDEs
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