Year: 2009
Author: Spike T. Lee, Hai-Wei Sun
Advances in Applied Mathematics and Mechanics, Vol. 1 (2009), Iss. 6 : pp. 845–861
Abstract
We consider pricing options in a jump-diffusion model which requires solving a partial integro-differential equation. Discretizing the spatial direction with a fourth order compact scheme leads to a linear system of ordinary differential equations. For the temporal direction, we utilize the favorable boundary value methods owing to their advantageous stability properties. In addition, the resulting large sparse system can be solved rapidly by the GMRES method with a circulant Strang-type preconditioner. Numerical results demonstrate the high order accuracy of our scheme and the efficiency of the preconditioned GMRES method.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.09-m09S06
Advances in Applied Mathematics and Mechanics, Vol. 1 (2009), Iss. 6 : pp. 845–861
Published online: 2009-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Partial integro-differential equation fourth order compact scheme boundary value method preconditioning Toeplitz matrix.
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