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

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

15 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
Number of pages	16
Journal	Journal of Scientific Computing
Volume	87
Issue number	1
Early online date	4 Mar 2021
DOIs	https://doi.org/10.1007/s10915-021-01438-7
Publication status	Published - Apr 2021

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SDG 9 Industry, Innovation, and Infrastructure

User-Defined Keywords

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

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10.1007/s10915-021-01438-7

Cite this

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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",

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AU - Ma, Shu

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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.

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KW - Exponential integrator

KW - High-order accuracy

KW - Nonlinear parabolic equation

KW - Nonsmooth initial data

KW - Variable stepsize

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

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