Mehdizadeh Khalsaraei, M., Osmani, N. (2017). A family of positive nonstandard numerical methods with application to Black-Scholes equation. Sahand Communications in Mathematical Analysis, 5(1), 31-40.

Mohammad Mehdizadeh Khalsaraei; Nashmil Osmani. "A family of positive nonstandard numerical methods with application to Black-Scholes equation". Sahand Communications in Mathematical Analysis, 5, 1, 2017, 31-40.

Mehdizadeh Khalsaraei, M., Osmani, N. (2017). 'A family of positive nonstandard numerical methods with application to Black-Scholes equation', Sahand Communications in Mathematical Analysis, 5(1), pp. 31-40.

Mehdizadeh Khalsaraei, M., Osmani, N. A family of positive nonstandard numerical methods with application to Black-Scholes equation. Sahand Communications in Mathematical Analysis, 2017; 5(1): 31-40.

A family of positive nonstandard numerical methods with application to Black-Scholes equation

^{}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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