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Volume 24, Issue 2
A Fast Finite Difference Method for Tempered Fractional Diffusion Equations

Xu Guo, Yutian Li & Hong Wang

DOI: 10.4208/cicp.OA-2018-0001

Commun. Comput. Phys., 24 (2018), pp. 531-556.

Published online: 2018-08

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  • Abstract

Using the idea of weighted and shifted differences, we propose a novel finite difference formula with second-order accuracy for the tempered fractional derivatives. For tempered fractional diffusion equations, the proposed finite difference formula yields an unconditionally stable scheme when an implicit Euler method is used. For the numerical simulation and as an application, we take the CGMYe model as an example. The numerical experiments show that second-order accuracy is achieved for both European and American options.

  • Keywords

Tempered fractional derivatives, fractional differential equations, method of characteristics, CGMYe model.

  • AMS Subject Headings

26A33, 35R11, 65M06, 65M12

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-24-531, author = {Xu Guo, Yutian Li and Hong Wang}, title = {A Fast Finite Difference Method for Tempered Fractional Diffusion Equations}, journal = {Communications in Computational Physics}, year = {2018}, volume = {24}, number = {2}, pages = {531--556}, abstract = {

Using the idea of weighted and shifted differences, we propose a novel finite difference formula with second-order accuracy for the tempered fractional derivatives. For tempered fractional diffusion equations, the proposed finite difference formula yields an unconditionally stable scheme when an implicit Euler method is used. For the numerical simulation and as an application, we take the CGMYe model as an example. The numerical experiments show that second-order accuracy is achieved for both European and American options.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2018-0001}, url = {http://global-sci.org/intro/article_detail/cicp/12251.html} }
TY - JOUR T1 - A Fast Finite Difference Method for Tempered Fractional Diffusion Equations AU - Xu Guo, Yutian Li & Hong Wang JO - Communications in Computational Physics VL - 2 SP - 531 EP - 556 PY - 2018 DA - 2018/08 SN - 24 DO - http://doi.org/10.4208/cicp.OA-2018-0001 UR - https://global-sci.org/intro/article_detail/cicp/12251.html KW - Tempered fractional derivatives, fractional differential equations, method of characteristics, CGMYe model. AB -

Using the idea of weighted and shifted differences, we propose a novel finite difference formula with second-order accuracy for the tempered fractional derivatives. For tempered fractional diffusion equations, the proposed finite difference formula yields an unconditionally stable scheme when an implicit Euler method is used. For the numerical simulation and as an application, we take the CGMYe model as an example. The numerical experiments show that second-order accuracy is achieved for both European and American options.

Xu Guo, Yutian Li and Hong Wang. (2018). A Fast Finite Difference Method for Tempered Fractional Diffusion Equations. Communications in Computational Physics. 24 (2). 531-556. doi:10.4208/cicp.OA-2018-0001
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