An ETD Crank-Nicolson method for reaction-diffusion systems

Authors

  • B. Kleefeld,

    1. Institut für Mathematik, Brandenburgische Technische Universität Cottbus, Postfach 101344, 03013 Cottbus, Germany
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  • A.Q.M. Khaliq,

    1. Department of Mathematical Sciences and Computational Science Program, Middle Tennessee State University, Murfreesboro, Tennessee 37132-0001
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  • B.A. Wade

    Corresponding author
    1. Department of Mathematical Sciences, University of Wisconsin–Milwaukee, Milwaukee, Wisconsin 53201-0413
    • Department of Mathematical Sciences, University of Wisconsin–Milwaukee, Milwaukee, Wisconsin 53201-0413
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Abstract

A novel Exponential Time Differencing Crank-Nicolson method is developed which is stable, second-order convergent, and highly efficient. We prove stability and convergence for semilinear parabolic problems with smooth data. In the nonsmooth data case, we employ a positivity-preserving initial damping scheme to recover the full rate of convergence. Numerical experiments are presented for a wide variety of examples, including chemotaxis and exotic options with transaction cost. © 2011Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2012

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