Time discretization of a tempered fractional Feynman-Kac equation with measure data

Weihua Deng, Buyang Li, Zhi Qian, Hong Wang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

9 Citations (Scopus)

Abstract

A feasible approach to study tempered anomalous dynamics is to analyze its functional distribution, which is governed by the tempered fractional Feynman-Kac equation. The main challenges of numerically solving the equation come from the time-space coupled nonlocal operators and the complex parameters involved. In this work, we introduce an efficient time-stepping method to discretize the tempered fractional Feynman-Kac equation by using the Laplace transform representation of convolution quadrature. Rigorous error estimate for the discrete solutions is carried out in the measure norm. Numerical experiments are provided to support the theoretical results.

Original languageEnglish
Pages (from-to)3249-3275
Number of pages27
JournalSIAM Journal on Numerical Analysis
Volume56
Issue number6
DOIs
Publication statusPublished - 20 Nov 2018

Keywords

  • Convergence
  • Convolution quadrature
  • Feynmann-Kac equation
  • Integral representation
  • Tempered fractional operators

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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