Exponential convolution quadrature for nonlinear subdiffusion equations with nonsmooth initial data

Buyang Li, Shu Ma

Research output: Journal article publicationJournal articleAcademic researchpeer-review

19 Citations (Scopus)

Abstract

An exponential type of convolution quadrature is proposed as a time-stepping method for the nonlinear subdiffusion equation with bounded measurable initial data. The method combines contour integral representation of the solution, quadrature approximation of contour integrals, multistep exponential integrators for ordinary differential equations, and locally refined stepsizes to resolve the initial singularity. The proposed k-step exponential convolution quadrature can have kth-order convergence for bounded measurable solutions of the nonlinear subdiffusion equation based on natural regularity of the solution with bounded measurable initial data.

Original languageEnglish
Pages (from-to)503–528
Number of pages26
JournalSIAM Journal on Numerical Analysis
Volume60
Issue number2
DOIs
Publication statusPublished - Mar 2022

Keywords

  • convolution quadrature
  • exponential integrator
  • high order
  • locally refined stepsizes
  • nonlinear
  • nonsmooth initial data
  • subdiffusion equation
  • time-fractional

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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