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Irrational approximations and their applications to partial differential equations in exterior domains,

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Abstract

A family of orthogonal systems of irrational functions on the semi-infinite interval is introduced. The proposed orthogonal systems are based on Jacobi polynomials through an irrational coordinate transform. This family of orthogonal systems offers great flexibility to match a wide range of asymptotic behaviors at infinity. Approximation errors by the basic orthogonal projection and various other orthogonal projections related to partial differential equations in unbounded domains are established. As an example of applications, a Galerkin approximation using the proposed irrational functions to an exterior problem is analyzed and implemented. Numerical results in agreement with our theoretical estimates are presented.

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Authors and Affiliations

  1. Department of Mathematics, Shanghai Normal University and Shanghai E-Institute for Computational Science, 200234, Shanghai, China

    Ben-yu Guo

  2. Department of Mathematics, Purdue University, West Lafayette, IN, 47907, USA

    Jie Shen

Authors
  1. Ben-yu Guo
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  2. Jie Shen
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Correspondence to Ben-yu Guo.

Additional information

The work of B.G. is supported in part by NSF of China, N.10471095, SF of Shanghai N.04JC14062, The Fund of Chinese Education Ministry N.20040270002, The Shanghai Leading Academic Discipline Project N. T0401, and The Funds for E-institutes of Shanghai Universities N.E03004.

The work of J.S. is supported in part by NSF Grants DMS-0311915, DMS-0509665 and Shanghai E-Institute for Computational Science.

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Guo, By., Shen, J. Irrational approximations and their applications to partial differential equations in exterior domains, . Adv Comput Math 28, 237–267 (2008). https://doi.org/10.1007/s10444-006-9020-5

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