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

Buyang Li; Shu Ma

doi:10.1007/s10915-021-01438-7

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

Buyang Li
, Shu Ma

Research output: Journal article publication › Journal article › Academic research › peer-review

13 Citations (Scopus)

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 k^th-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 language	English
Article number	23
Pages (from-to)	1-16
Number of pages	16
Journal	Journal of Scientific Computing
Volume	87
Issue number	1
DOIs	https://doi.org/10.1007/s10915-021-01438-7
Publication status	Published - 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
General Engineering
Computational Theory and Mathematics
Computational Mathematics
Applied Mathematics

More information

10.1007/s10915-021-01438-7

http://hdl.handle.net/10397/93865

Cite this

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title = "A High-order Exponential Integrator for Nonlinear Parabolic Equations with Nonsmooth Initial Data",

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.",

keywords = "Discontinuous initial data, Exponential integrator, High-order accuracy, Nonlinear parabolic equation, Nonsmooth initial data, Variable stepsize",

author = "Buyang Li and Shu Ma",

note = "Funding Information: This work is partially supported by the Hong Kong Research Grants Council (GRF project No. 15300519) and an internal grant of the university (project code ZZKK) Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC part of Springer Nature.",

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AU - Ma, Shu

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Y1 - 2021/4

N2 - 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.

AB - 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.

KW - Discontinuous initial data

KW - Exponential integrator

KW - High-order accuracy

KW - Nonlinear parabolic equation

KW - Nonsmooth initial data

KW - Variable stepsize

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DO - 10.1007/s10915-021-01438-7

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AN - SCOPUS:85102111438

SN - 0885-7474

VL - 87

SP - 1

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ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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