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Stability of central finite difference schemes on non-uniform grids for the Black-Scholes PDE with Neumann boundary condition
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| Abstract |
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| This paper concerns the numerical solution of the BlackScholes PDE with a Neumann boundary condition on the right boundary. We consider finite difference schemes for the semi-discretization, which leads to a system of ODEs with corresponding matrix M. In this paper stability bounds for exp(tM) (t ≥ 0) are proved. A scaled version of the Euclidean norm, denoted by ‖ ⋅ ‖H is considered. The advection and diffusion term of the PDE are analyzed separately. It turns out that the Neumann boundary condition leads to a growth of ‖exp(tM)‖H with the number of grid points m for the pure advection problem. |
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English
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| Source (journal) |
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AIP conference proceedings / American Institute of Physics. - New York |
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| Publication |
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New York : 2012
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0094-243X
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| Volume/pages |
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1479(2012), p. 2178-2181
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| ISI |
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000310698100514
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| Full text (Publisher's DOI) |
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| Full text (open access) |
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