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Domain Decomposition Spectral Method for Mixed Inhomogeneous Boundary Value Problems of High Order Differential Equations on Unbounded Domains

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Abstract

In this paper, we develop domain decomposition spectral method for mixed inhomogeneous boundary value problems of high order differential equations defined on unbounded domains. We introduce an orthogonal family of new generalized Laguerre functions, with the weight function x α, α being any real number. The corresponding quasi-orthogonal approximation and Gauss-Radau type interpolation are investigated, which play important roles in the related spectral and collocation methods. As examples of applications, we propose the domain decomposition spectral methods for two fourth order problems, and the spectral method with essential imposition of boundary conditions. The spectral accuracy is proved. Numerical results demonstrate the effectiveness of suggested algorithms.

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Authors and Affiliations

  1. Jiangsu Normal University, Xuzhou, 221116, China

    Chao Zhang

  2. Shanghai Normal University, Shanghai, 200234, China

    Ben-yu Guo

  3. Scientific Computing Key Laboratory, Division of Computational Science of E-institute, Shanghai Universities, Shanghai, China

    Ben-yu Guo

Authors
  1. Chao Zhang
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  2. Ben-yu Guo
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Correspondence to Ben-yu Guo.

Additional information

The work of C. Zhang is supported in part by NSF of China No. 11171227 and Research Fund for young teachers of Jiangsu Normal University No. 11XLR27.

The work of B.-y. Guo is supported in part by NSF of China No. 11171227, Fund for Doctor Authority of Chinese Educational Ministry No. 20080270001, Shanghai Leading Academic Discipline Project No. S30405, and Fund for E-institute of Shanghai Universities No. E03004.

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Zhang, C., Guo, By. Domain Decomposition Spectral Method for Mixed Inhomogeneous Boundary Value Problems of High Order Differential Equations on Unbounded Domains. J Sci Comput 53, 451–480 (2012). https://doi.org/10.1007/s10915-012-9581-z

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  • DOI: https://doi.org/10.1007/s10915-012-9581-z

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