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

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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 \(k^{\mathrm{th}}\)-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.

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Authors and Affiliations

  1. Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Hong Kong

    Buyang Li & Shu Ma

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  1. Buyang Li
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  2. Shu Ma
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Correspondence to Buyang Li.

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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)

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Li, B., Ma, S. A High-order Exponential Integrator for Nonlinear Parabolic Equations with Nonsmooth Initial Data. J Sci Comput 87, 23 (2021). https://doi.org/10.1007/s10915-021-01438-7

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