Green’s function for the boundary value problem of the static Klein-Gordon equation stated on a rectangular region and its convergence analysis

This study is motivated by solving the inverse boundary problem of the static Klein-Gordon equation (SKGE), which usually occurs in data assimilation problems. For the purpose of obtaining boundary conditions, the pro forma solution of the problem is provided by using Green’s function. The represent...

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Bibliographic Details
Published inBoundary value problems Vol. 2017; no. 1; pp. 1 - 14
Main Authors Cheng, Hao, Mu, Xiyu, Jiang, Hua, Liu, Guoqing, Wei, Ming
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 18.05.2017
Hindawi Limited
SpringerOpen
Subjects
Analysis
Approximations and Expansions
Boundary conditions
boundary value problem
Boundary value problems
Convergence
Difference and Functional Equations
Green's functions
Green’s function
inverse problem
Klein-Gordon equation
Mathematics
Mathematics and Statistics
Method of images
Ordinary Differential Equations
Partial Differential Equations
rectangular region
Representations
inverse problem
Green’s function
rectangular region
Klein-Gordon equation
26B20
35J08
boundary value problem
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Summary:This study is motivated by solving the inverse boundary problem of the static Klein-Gordon equation (SKGE), which usually occurs in data assimilation problems. For the purpose of obtaining boundary conditions, the pro forma solution of the problem is provided by using Green’s function. The representation in double series of Green’s function for the SKGE on a rectangular region is obtained by means of the method of images. Convergence analysis shows that the representation is uniformly convergent, which is computer friendly, and can be applied to approximate computations.
ISSN:1687-2770
1687-2762
1687-2770
DOI:10.1186/s13661-017-0803-z