On high-order schemes for tempered fractional partial differential equations

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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.

Original languageEnglish
Pages (from-to)459-481
Number of pages23
JournalApplied Numerical Mathematics
Volume165
DOIs
Publication statusPublished - 2021

Keywords

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

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