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Numerical methods for a class of nonlinear integro-differential equations

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Abstract

In a previous article (Glowinski, J. Math. Anal. Appl. 41, 67–96, 1973) the first author discussed several methods for the numerical solution of nonlinear equations of the integro-differential type with periodic boundary conditions. In this article we discuss an alternative methodology largely based on the Strang’s symmetrized operator-splitting scheme. Several numerical experiments suggest that the new method is robust and accurate. It is also easier to implement than the various methods discussed by Glowinski in J. Math. Anal. Appl. 41, 67–96 (1973).

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Acknowledgements

The authors would like to thank the anonymous referee for helpful comments and suggestions. This work was supported in part by National Science Foundation, grant number 0908528 (L.S. & M.S.).

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Authors and Affiliations

  1. Department of Mathematics, University of Houston, Houston, TX, 77204, USA

    R. Glowinski

  2. Department of Mathematics, University of Houston, Clear Lake, Houston, TX, 77058, USA

    L. Shiau & M. Sheppard

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  1. R. Glowinski
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  2. L. Shiau
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  3. M. Sheppard
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Correspondence to L. Shiau.

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Glowinski, R., Shiau, L. & Sheppard, M. Numerical methods for a class of nonlinear integro-differential equations. Calcolo 50, 17–33 (2013). https://doi.org/10.1007/s10092-012-0056-2

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