On high-order schemes for tempered fractional partial differential equations

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On high-order schemes for tempered fractional partial differential equations

Journal Article (2021)

Author(s)

Linlin Bu (TU Delft - Electrical Engineering, Mathematics and Computer Science, Xi’an Jiaotong University)

Cornelis W. Oosterlee (TU Delft - Electrical Engineering, Mathematics and Computer Science, Universiteit Utrecht)

Research Group

Numerical Analysis

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

DOI related publication

https://doi.org/10.1016/j.apnum.2021.03.008 Final published version

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https://resolver.tudelft.nl/uuid:0de5505d-c8b9-4a3d-850f-ee13b21c0a4b

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Publication Year

2021

Language

English

Research Group

Numerical Analysis

Journal title

Applied Numerical Mathematics

Volume number

165

Pages (from-to)

459-481

Downloads counter

161

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.