On a finite difference analogue of a singular boundary value problem.
Herceg, Dragoslav, Krejić, Nataša, Maličić, Helena (2000)
Novi Sad Journal of Mathematics
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Herceg, Dragoslav, Krejić, Nataša, Maličić, Helena (2000)
Novi Sad Journal of Mathematics
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Vulanović, Relja (2001)
Novi Sad Journal of Mathematics
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Surla, Katarina, Herceg, Dragoslav, Maličić, Helena (2001)
Novi Sad Journal of Mathematics
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Ciegis, R., Starikovicius, V. (2001)
Computational Methods in Applied Mathematics
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Uri Ascher (1985)
Numerische Mathematik
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Milev, Mariyan, Tagliani, Aldo (2010)
Serdica Mathematical Journal
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2000 Mathematics Subject Classification: 65M06, 65M12. In this paper we explore the numerical diffusion introduced by two nonstandard finite difference schemes applied to the Black-Scholes partial differential equation for pricing discontinuous payoff and low volatility options. Discontinuities in the initial conditions require applying nonstandard non-oscillating finite difference schemes such as the exponentially fitted finite difference schemes suggested by D. Duffy and...
Florian Mehats (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
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We present here a discretization of a nonlinear oblique derivative boundary value problem for the heat equation in dimension two. This finite difference scheme takes advantages of the structure of the boundary condition, which can be reinterpreted as a Burgers equation in the space variables. This enables to obtain an energy estimate and to prove the convergence of the scheme. We also provide some numerical simulations of this problem and a numerical study of the stability of the...
Katarina Surla, Zorica Uzelac (1993)
Publications de l'Institut Mathématique
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Guevara-Jordan, J.M., Rojas, S., Freites-Villegas, M., Castillo, J.E. (2005)
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Illner, R., Rjasanow, S. (1999)
Documenta Mathematica
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Annales Polonici Mathematici
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