On high-order schemes for tempered fractional partial differential equations

Linlin Bu*, Cornelis W. Oosterlee

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review


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 languageEnglish
Pages (from-to)459-481
Number of pages23
JournalApplied Numerical Mathematics
Publication statusPublished - Jul 2021


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


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