Uniformly Convergent Difference Schemes for Singularly Perturbed Parabolic Diffusion-Convection Problems Without Turning Points.
Eugene O'Riordan, Martin Stynes (1987)
Numerische Mathematik
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Eugene O'Riordan, Martin Stynes (1987)
Numerische Mathematik
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Dehghan, Mehdi (2001)
Mathematical Problems in Engineering
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Liu, Don, Kuang, Weijia, Tangborn, Andrew (2009)
Advances in Mathematical Physics
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Dehghan, Mehdi (2002)
Mathematical Problems in Engineering
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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...
Bertram Düring, Michel Fournié, Ansgar Jüngel (2004)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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A high-order compact finite difference scheme for a fully nonlinear parabolic differential equation is analyzed. The equation arises in the modeling of option prices in financial markets with transaction costs. It is shown that the finite difference solution converges locally uniformly to the unique viscosity solution of the continuous equation. The proof is based on a careful study of the discretization matrices and on an abstract convergence result due to Barles and Souganides. ...
Robert Eymard, Cindy Guichard, Raphaèle Herbin (2012)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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In this paper, we study some discretization schemes for diffusive flows in heterogeneous anisotropic porous media. We first introduce the notion of gradient scheme, and show that several existing schemes fall into this framework. Then, we construct two new gradient schemes which have the advantage of a small stencil. Numerical results obtained for real reservoir meshes show the efficiency of the new schemes, compared to existing ones.
Guevara-Jordan, J.M., Rojas, S., Freites-Villegas, M., Castillo, J.E. (2007)
Advances in Difference Equations [electronic only]
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Vinod Kumar, Rajesh Bawa, Arvind Lal (2014)
International Journal of Applied Mathematics and Computer Science
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A. Fitzke (1970)
Annales Polonici Mathematici
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