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An efficient nonstandard numerical method with positivity preserving property | ||
| Journal of Mathematical Modeling | ||
| مقاله 3، دوره 4، شماره 2، اسفند 2016، صفحه 161-169 اصل مقاله (1.98 M) | ||
| نوع مقاله: Research Article | ||
| نویسندگان | ||
| Mohammad Mehdizadeh Khalsaraei* 1؛ Reza Shokri Jahandizi2 | ||
| 1Department of Mathematics, Faculty of Science, University of Maragheh Maragheh, Iran | ||
| 2Department of Mathematics, Faculty of Science, University of Maragheh, Maragheh, Iran | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| positivity preserving؛ nonstandard finite differences؛ Black-Scholes equation | ||
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