University of MaraghehSahand Communications in Mathematical Analysis2322-580705120170101A family of positive nonstandard numerical methods with application to Black-Scholes equation31401933510.22130/scma.2017.19335ENMohammad Mehdizadeh KhalsaraeiDepartment of Mathematics, Faculty of Science, University of Maragheh, Maragheh, Iran.Nashmil OsmaniDepartment 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