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.
"Exponential Time Integration and Second-Order Difference Scheme for a Generalized Black-Scholes Equation." J. Appl. Math. 2012 1 - 12, 2012. https://doi.org/10.1155/2012/796814