Association schemes. I
Luboš Bauer (1981)
Archivum Mathematicum
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Luboš Bauer (1981)
Archivum Mathematicum
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Mustafa, Ghulam, Khan, Faheem (2009)
Abstract and Applied Analysis
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Kyei, Yaw, Roop, John Paul, Tang, Guoqing (2010)
Advances in Numerical Analysis
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Janenko, N. N.
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Milev, Mariyan, Tagliani, Aldo (2010)
Serdica Mathematical Journal
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2000 Mathematics Subject Classification: 65M06, 65M12. The paper is devoted to pricing options characterized by discontinuities in the initial conditions of the respective Black-Scholes partial differential equation. Finite difference schemes are examined to highlight how discontinuities can generate numerical drawbacks such as spurious oscillations. We analyze the drawbacks of the Crank-Nicolson scheme that is most frequently used numerical method in Finance because of its...
Gordeziani, E., Gordeziani, D. (2000)
Bulletin of TICMI
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Michael Breuss (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
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We discuss the occurrence of oscillations when using central schemes of the Lax-Friedrichs type (LFt), Rusanov's method and the staggered and non-staggered second order Nessyahu-Tadmor (NT) schemes. Although these schemes are monotone or TVD, respectively, oscillations may be introduced at local data extrema. The dependence of oscillatory properties on the numerical viscosity coefficient is investigated rigorously for the LFt schemes, illuminating also the properties of Rusanov's...