Commun. Comput. Phys., 16 (2014), pp. 1102-1115.


Dirichlet-to-Neumann Mapping for the Characteristic Elliptic Equations with Symmetric Periodic Coefficients

Jingsu Kang 1, Meirong Zhang 1, Chunxiong Zheng 1*

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

Received 11 December 2013; Accepted (in revised version) 11 April 201
Available online 12 August 2014
doi:10.4208/cicp.111213.110414a

Abstract

Based on the numerical evidences, an analytical expression of the Dirichlet-to-Neumann mapping in the form of infinite product was first conjectured for the one-dimensional characteristic Schrodinger equation with a sinusoidal potential in [Commun. Comput. Phys., 3(3): 641-658, 2008]. It was later extended for the general second-order characteristic elliptic equations with symmetric periodic coefficients in [J. Comp. Phys., 227: 6877-6894, 2008]. In this paper, we present a proof for this Dirichlet-to-Neumann mapping.

AMS subject classifications: 65M99, 81-08

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Key words: Dirichlet-to-Neumann mapping, Schrodinger equation, symmetric periodic potentials, absorbing boundary conditions.

*Corresponding author.
Email: 691675583@qq.com (J. Kang), mzhang@math.tsinghua.edu.cn (M. Zhang), czheng@math.tsinghua.edu.cn (C. Zheng)
 

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