A High-order Exponential Integrator for Nonlinear Parabolic Equations with Nonsmooth Initial Data

Buyang Li, Shu Ma

Research output: Journal article publicationJournal articleAcademic researchpeer-review

Abstract

A variable stepsize exponential multistep integrator, with contour integral approximation of the operator-valued exponential functions, is proposed for solving semilinear parabolic equations with nonsmooth initial data. By this approach, the exponential k-step method would have kth-order convergence in approximating a mild solution, possibly nonsmooth at the initial time. In consistency with the theoretical analysis, a numerical example shows that the method can achieve high-order convergence in the maximum norm for semilinear parabolic equations with discontinuous initial data.

Original languageEnglish
Article number23
Pages (from-to)1-16
Number of pages16
JournalJournal of Scientific Computing
Volume87
Issue number1
DOIs
Publication statusPublished - Apr 2021

Keywords

  • Discontinuous initial data
  • Exponential integrator
  • High-order accuracy
  • Nonlinear parabolic equation
  • Nonsmooth initial data
  • Variable stepsize

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • Engineering(all)
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

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