@article{Cen2022, 
author = {Zhongdi Cen and Jian Huang and Aimin Xu},
title = {A posteriori grid method for a time-fractional Black-Scholes equation},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {12},
pages = {20962-20978},
keywords = {option valuation, Black-Scholes equation, fractional differential equation, a posteriori grid, a posteriori error analysis},
url = {https://www.sciopen.com/article/10.3934/math.20221148},
doi = {10.3934/math.20221148},
abstract = {In this paper, a posteriori grid method for solving a time-fractional Black-Scholes equation governing European options is studied. The possible singularity of the exact solution complicates the construction of the discretization scheme for the time-fractional Black-Scholes equation. The  L1 method on an arbitrary grid is used to discretize the time-fractional derivative and the central difference method on a piecewise uniform grid is used to discretize the spatial derivatives. Stability properties and a posteriori error analysis for the discrete scheme are studied. Then, an adapted a posteriori grid is constructed by using a grid generation algorithm based on a posteriori error analysis. Numerical experiments show that the  L1 method on an adapted a posteriori grid is more accurate than the method on the uniform grid.}
}