2024 : 11 : 22

Mohammad Mehdizadeh

Academic rank: Professor
ORCID:
Education: PhD.
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Faculty: 1
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Research

Title
An efficient nonstandard numerical method with positivity preserving property
Type
JournalPaper
Keywords
positivity preserving, nonstandard finite differences, Black-Scholes equation.
Year
2016
Journal Journal of Mathematical Modeling
DOI
Researchers Mohammad Mehdizadeh ، Reza Shokri Jahandizi

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.