1
Department of Mathematics, Faculty of Science, University of Maragheh Maragheh, Iran
2
Department of Mathematics, Faculty of Science, University of Maragheh, Maragheh, Iran
Abstract
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.
Mehdizadeh Khalsaraei, M., & Shokri Jahandizi, R. (2016). An efficient nonstandard numerical method with positivity preserving property. Journal of Mathematical Modeling, 4(2), 161-169.
MLA
Mohammad Mehdizadeh Khalsaraei; Reza Shokri Jahandizi. "An efficient nonstandard numerical method with positivity preserving property". Journal of Mathematical Modeling, 4, 2, 2016, 161-169.
HARVARD
Mehdizadeh Khalsaraei, M., Shokri Jahandizi, R. (2016). 'An efficient nonstandard numerical method with positivity preserving property', Journal of Mathematical Modeling, 4(2), pp. 161-169.
VANCOUVER
Mehdizadeh Khalsaraei, M., Shokri Jahandizi, R. An efficient nonstandard numerical method with positivity preserving property. Journal of Mathematical Modeling, 2016; 4(2): 161-169.
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