On high-order schemes for tempered fractional partial differential equations

2020/09/15 by Linlin Bu, Cornelis W. Oosterlee, Bu, Linlin +1
Mathematics · #Differential Equations and Numerical Methods #FOS: Mathematics #Fractional Differential Equations Solutions #Nonlinear Differential Equations Analysis #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2009.07321

openalex publication_date 2020/09/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we propose third-order semi-discretized schemes in space based on the tempered weighted and shifted Grünwald 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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