An efficient nonstandard numerical method with positivity preserving property
محل انتشار: مجله مدلسازی ریاضی، دوره: 4، شماره: 2
سال انتشار: 1395
نوع سند: مقاله ژورنالی
زبان: انگلیسی
مشاهده: 65
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شناسه ملی سند علمی:
JR_JMMO-4-2_003
تاریخ نمایه سازی: 19 خرداد 1403
چکیده مقاله:
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.
کلیدواژه ها:
نویسندگان
Mohammad Mehdizadeh Khalsaraei
Department of Mathematics, Faculty of Science, University of Maragheh Maragheh, Iran
Reza Shokri Jahandizi
Department of Mathematics, Faculty of Science, University of Maragheh, Maragheh, Iran