@Article{AAMM-11-2,
author = {Limei, Li and Lapin, Alexander and Zhang, Shuhua},
title = {Alternating Direction Implicit Finite Element Method for Multi-Dimensional Black-Scholes Models},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2019},
volume = {11},
number = {2},
pages = {535--558},
abstract = {<p style="text-align: justify;">A new numerical method is proposed and investigated for solving two- dimensional Black-Scholes option pricing model. This model is represented&nbsp; by Dirichlet initial-boundary value problem in a rectangular domain for a parabolic equation with advection-diffusion operator containing mixed derivatives. It is approximated by using a finite element method in spatial variables and alternating direction implicit (ADI) method in time variable. The ADI scheme is based on the semi-implicit approximation. The stability and convergence of the constructed scheme is proved rigorously. The provided computational results demonstrate the efficiency and high accuracy of the proposed method.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.OA-2018-0144},
url = {https://global-sci.com/article/73100/alternating-direction-implicit-finite-element-method-for-multi-dimensional-black-scholes-models}
}