On high-order schemes for tempered fractional partial differential equations

被引：4
|
作者：
Bu, Linlin [1 ,2 ]
Oosterlee, Cornelis W. [2 ,3 ]
机构：
[1] Xi An Jiao Tong Univ, Sch Math & Stat, Xian 710049, Shaanxi, Peoples R China
[2] Delft Univ Technol, Appl Math DIAM, Delft, Netherlands
[3] Univ Utrecht, Math Inst, Utrecht, Netherlands
来源：
APPLIED NUMERICAL MATHEMATICS | 2021年 / 165卷
关键词：
High-order tempered-WSGD operator; The tempered fractional derivative; Stability; Convergence;
D O I：
10.1016/j.apnum.2021.03.008
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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. (C) 2021 IMACS. Published by Elsevier B.V. All rights reserved.
引用
收藏
页码：459 / 481
页数：23
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