%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