An Exponential Spectral Method Using VP Means for Semilinear Subdiffusion Equations with Rough Data

Buyang Li, Yanping Lin, Shu Ma, Qiqi Rao*

*Corresponding author for this work

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

3 Citations (Scopus)
42 Downloads (CityUHK Scholars)

Abstract

A new spectral method is constructed for the linear and semilinear subdiffusion equations with possibly discontinuous rough initial data. The new method effectively combines several computational techniques, including the contour integral representation of the solutions, the quadrature approximation of contour integrals, the exponential integrator using the de la Vallée Poussin means of the source function, and a decomposition of the time interval geometrically refined towards the singularity of the solution and the source function. Rigorous error analysis shows that the proposed method has spectral convergence for the linear and semilinear subdiffusion equations with bounded measurable initial data and possibly singular source functions under the natural regularity of the solutions. © 2023 Society for Industrial and Applied Mathematics Publications. All rights reserved.
Original languageEnglish
Pages (from-to)2305-2326
JournalSIAM Journal on Numerical Analysis
Volume61
Issue number5
Online published9 Oct 2023
DOIs
Publication statusPublished - 2023

Research Keywords

  • contour integral
  • convolution quadrature
  • exponential integrator
  • geometric decomposition
  • quadrature approximation
  • semilinear subdiffusion equation
  • singularity
  • spectral method
  • VP means

Publisher's Copyright Statement

  • COPYRIGHT TERMS OF DEPOSITED FINAL PUBLISHED VERSION FILE: © 2023 Society for Industrial and Applied Mathematics.

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