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Nonlinear Artificial Boundary Conditions

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Artificial Boundary Method

Abstract

In this chapter, we discuss the nonlinear ABCs for Burgers equation, Kardar-Parisi-Zhang equation, and Schrödinger equation on unbounded domains. By using artificial boundaries, the original problems are reduced to initial boundary value problems on bounded computational domains. Nonlinear boundary conditions on the artificial boundaries are obtained, and then the finite difference method is applied to solve the reduced problems. Some stability results are also given.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, China

    Houde Han

  2. Department of Mathematics, Hong Kong Baptist University, Kowloon, Hong Kong, China

    Xiaonan Wu

Authors
  1. Houde Han
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  2. Xiaonan Wu
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© 2013 Tsinghua University Press, Beijing and Springer-Verlag Berlin Heidelberg

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Han, H., Wu, X. (2013). Nonlinear Artificial Boundary Conditions. In: Artificial Boundary Method. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35464-9_9

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