A Fast Finite Difference Method for Tempered Fractional Diffusion Equations (Communications in Computational Physics, 2018)
Using the idea of weighted and shifted differences, we propose a novel finite difference formula with second-order accuracy for the tempered fractional derivatives. For tempered fractional diffusion equations, the proposed finite difference formula yields an unconditionally stable scheme when an implicit Euler method is used.For the numerical simulation and as an application, we take the CGMYe model as anexample. The numerical experiments show that second-order accuracy is achieved forboth European and American options.
Keywords: Tempered fractional derivatives; fractional differential equations; method of characteristics; CGMYe model.