Generalized Jacobi rational spectral methods with essentialimposition of Neumann boundary conditions in unbounded domains

Zhong-Qing Wang; Jing-Xia Wu

doi:10.3934/dcdsb.2012.17.325

Article Contents

2012, Volume 17, Issue 1: 325-346. Doi: 10.3934/dcdsb.2012.17.325

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Generalized Jacobi rational spectral methods with essential imposition of Neumann boundary conditions in unbounded domains

Zhong-Qing Wang^1, and
Jing-Xia Wu^1,

1.
Department of Mathematics, Shanghai Normal University, Shanghai, 200234

Received: July 31, 2010

Revised: January 31, 2011

Published: December 2011

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Abstract

In this paper, we develop several generalized Jacobi rational spectral methods with essential imposition of Neumann boundary conditions for one/two dimensional Neumann problems. Some basic results on the generalized Jacobi rational approximations for Neumann problems are established, which play important roles in the related spectral methods. Three model problems are considered. The convergence of proposed schemes is proved. Numerical results demonstrate their spectral accuracy and efficiency.

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Mathematics Subject Classification: Primary: 65M70, 41A20, 35J25.

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