%0 Journal Article
%T An efficient nonstandard numerical method with positivity preserving property
%J Journal of Mathematical Modeling
%I University of Guilan
%Z 2345-394X
%A Mehdizadeh Khalsaraei, Mohammad
%A Shokri Jahandizi, Reza
%D 2016
%\ 10/29/2016
%V 4
%N 2
%P 161-169
%! An efficient nonstandard numerical method with positivity preserving property
%K positivity preserving
%K nonstandard finite differences
%K Black-Scholes equation
%R
%X Classical explicit finite difference schemes are unsuitable for the solution of the famous Black-Scholes partial differential equation, since they impose severe restrictions on the time step. Furthermore, they may produce spurious oscillations in the solution. We propose a new scheme that is free of spurious oscillations and guarantees the positivity of the solution for arbitrary stepsizes. The proposed method is constructed based on a nonstandard discretization of the spatial derivatives and is applicable to Black-Scholes equation in the presence of discontinues initial conditions.
%U https://jmm.guilan.ac.ir/article_1902_35066bb8835401ef74cc749daafbb5f2.pdf