On high-order schemes for tempered fractional partial differential equations

Linlin Bu; Cornelis W. Oosterlee

doi:10.1016/j.apnum.2021.03.008

On high-order schemes for tempered fractional partial differential equations

Linlin Bu^*, Cornelis W. Oosterlee

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

In this paper, we propose third-order semi-discretized schemes in space based on the tempered weighted and shifted Grunwald difference (tempered-WSGD) operators for the tempered fractional diffusion equation. We also show stability and convergence analysis for the fully discrete scheme based a Crank–Nicolson scheme in time. A third-order scheme for the tempered Black–Scholes equation is also proposed and tested numerically. Some numerical experiments are carried out to confirm accuracy and effectiveness of these proposed methods.

Original language	English
Pages (from-to)	459-481
Number of pages	23
Journal	Applied Numerical Mathematics
Volume	165
DOIs	https://doi.org/10.1016/j.apnum.2021.03.008
Publication status	Published - Jul 2021

Bibliographical note

Funding Information:
L. Bu would like to thank the China Scholarship Council (CSC No. 201906280196 ) for the financial support.

Publisher Copyright:
© 2021

Funding

L. Bu would like to thank the China Scholarship Council (CSC No. 201906280196 ) for the financial support.

Keywords

Convergence
High-order tempered-WSGD operator
Stability
The tempered fractional derivative

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10.1016/j.apnum.2021.03.008

1-s2.0-S0168927421000787-mainFinal published version, 1.12 MBLicence: Taverne

Cite this

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title = "On high-order schemes for tempered fractional partial differential equations",

abstract = "In this paper, we propose third-order semi-discretized schemes in space based on the tempered weighted and shifted Grunwald difference (tempered-WSGD) operators for the tempered fractional diffusion equation. We also show stability and convergence analysis for the fully discrete scheme based a Crank–Nicolson scheme in time. A third-order scheme for the tempered Black–Scholes equation is also proposed and tested numerically. Some numerical experiments are carried out to confirm accuracy and effectiveness of these proposed methods.",

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author = "Linlin Bu and Oosterlee, {Cornelis W.}",

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AU - Oosterlee, Cornelis W.

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AB - In this paper, we propose third-order semi-discretized schemes in space based on the tempered weighted and shifted Grunwald difference (tempered-WSGD) operators for the tempered fractional diffusion equation. We also show stability and convergence analysis for the fully discrete scheme based a Crank–Nicolson scheme in time. A third-order scheme for the tempered Black–Scholes equation is also proposed and tested numerically. Some numerical experiments are carried out to confirm accuracy and effectiveness of these proposed methods.

KW - Convergence

KW - High-order tempered-WSGD operator

KW - Stability

KW - The tempered fractional derivative

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SP - 459

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JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

ER -

On high-order schemes for tempered fractional partial differential equations

Abstract

Bibliographical note

Funding

Keywords

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