An unconditionally positivity preserving scheme for advection–diffusion reaction equations
نویسندگان
چکیده
منابع مشابه
Positivity-preserving nonstandard finite difference Schemes for simulation of advection-diffusion reaction equations
Systems in which reaction terms are coupled to diffusion and advection transports arise in a wide range of chemical engineering applications, physics, biology and environmental. In these cases, the components of the unknown can denote concentrations or population sizes which represent quantities and they need to remain positive. Classical finite difference schemes may produce numerical drawback...
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This paper deals with the numerical analysis of nonlinear Black-Scholes equation with transaction costs. An unconditionally stable and monotone splitting method, ensuring positive numerical solution and avoiding unstable oscillations, is proposed. This numerical method is based on the LOD-Backward Euler method which allows us to solve the discrete equation explicitly. The numerical results for ...
متن کاملpositivity-preserving nonstandard finite difference schemes for simulation of advection-diffusion reaction equations
systems in which reaction terms are coupled to diffusion and advection transports arise in awide range of chemical engineering applications, physics, biology and environmental. in these cases, thecomponents of the unknown can denote concentrations or population sizes which represent quantities andthey need to remain positive. classical finite difference schemes may produce numerical drawbacks s...
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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...
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Article history: Received 26 February 2014 Received in revised form 20 August 2014 Accepted 26 August 2014 Available online 3 September 2014
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ژورنال
عنوان ژورنال: Mathematical and Computer Modelling
سال: 2013
ISSN: 0895-7177
DOI: 10.1016/j.mcm.2011.05.005