A Fast Finite Difference Method for Tempered Fractional Diffusion Equations

A Fast Finite Difference Method for Tempered Fractional Diffusion Equations

Year:    2018

Communications in Computational Physics, Vol. 24 (2018), Iss. 2 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.OA-2018-0001

Communications in Computational Physics, Vol. 24 (2018), Iss. 2 : pp. 531–556

Published online:    2018-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    26

Keywords:    Tempered fractional derivatives fractional differential equations method of characteristics CGMYe model.