a family of positive nonstandard numerical methods with application to black-scholes equation

Authors

mohammad mehdizadeh khalsaraei

department of mathematics, faculty of science, university of maragheh, maragheh, iran. nashmil osmani

department of mathematics, faculty of science, university of maragheh, maragheh, iran.

abstract

nonstandard 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.

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Journal title:
sahand communications in mathematical analysis

جلد ۵، شماره ۱، صفحات ۳۱-۴۰

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