TY - JOUR
T1 - A Fast Finite Difference Method for Tempered Fractional Diffusion Equations
AU - Xu Guo, Yutian Li & Hong Wang
JO - Communications in Computational Physics
VL - 2
SP - 531
EP - 556
PY - 2018
DA - 2018/08
SN - 24
DO - http://doi.org/10.4208/cicp.OA-2018-0001
UR - https://global-sci.org/intro/article_detail/cicp/12251.html
KW - Tempered fractional derivatives, fractional differential equations, method of characteristics, CGMYe model.
AB - <p style="text-align: justify;">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 an
example. The numerical experiments show that second-order accuracy is achieved for
both European and American options.</p>