Error analysis of an L2-type method on graded meshes for semilinear subdiffusion equations

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Abstract

A semilinear initial–boundary value problem with a Caputo time derivative of fractional order α∈(0,1) is considered, solutions of which typically exhibit a singular behaviour at an initial time. For an L2-type discretization of order 3−α, we give sharp pointwise-in-time error bounds on graded temporal meshes with arbitrary degree of grading.

Original languageEnglish
Article number109306
JournalApplied Mathematics Letters
Volume160
DOIs
Publication statusPublished - Feb 2025

Keywords

  • Graded temporal mesh
  • L2 scheme
  • Pointwise-in-time error bounds
  • Semilinear
  • Subdiffusion equation

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