TY - JOUR
T1 - On high-order schemes for tempered fractional partial differential equations
AU - Bu, Linlin
AU - Oosterlee, Cornelis W.
PY - 2021
Y1 - 2021
N2 - 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.
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
UR - http://www.scopus.com/inward/record.url?scp=85102880399&partnerID=8YFLogxK
U2 - 10.1016/j.apnum.2021.03.008
DO - 10.1016/j.apnum.2021.03.008
M3 - Article
AN - SCOPUS:85102880399
SN - 0168-9274
VL - 165
SP - 459
EP - 481
JO - Applied Numerical Mathematics
JF - Applied Numerical Mathematics
ER -