University of MaraghehSahand Communications in Mathematical Analysis2322-580705120170101A family of positive nonstandard numerical methods with application to Black-Scholes equation31401933510.22130/scma.2017.19335ENMohammadMehdizadeh KhalsaraeiDepartment of Mathematics, Faculty of Science, University of Maragheh, Maragheh, Iran.NashmilOsmaniDepartment of Mathematics, Faculty of Science, University of Maragheh, Maragheh, Iran.Journal Article20151227Nonstandard finite difference schemes for the Black-Scholes partial differential equation preserving the positivity property are proposed. Computationally simple schemes are derived by using a nonlocal approximation in the reaction term of the Black-Scholes equation. Unlike the standard methods, the solutions of new proposed schemes are positive and free of the spurious oscillations.http://scma.maragheh.ac.ir/article_19335_cf08f2d957449d24abc0378c987a3ca6.pdf