Geodesic
Reproducing kernel methods for solving linear initial-boundary-value problems
Electronic journal of differential equations, Tome 2008 (2008)
In this paper, a reproducing kernel with polynomial form is used for finding analytical and approximate solutions of a second-order hyperbolic equation with linear initial-boundary conditions. The analytical solution is represented as a series in the reproducing kernel space, and the approximate solution is obtained as an n-term summation. Error estimates are proved to converge to zero in the sense of the space norm, and a numerical example is given to illustrate the method.
Classification : 35A35, 35A45, 35G05, 65N99
Keywords: hyperbolic equation, linear initial-boundary conditions, reproducing kernel space 
@article{EJDE_2008__2008__a16,
     author = {Yang,  Li-Hong and Lin,  Yingzhen},
     title = {Reproducing kernel methods for solving linear initial-boundary-value problems},
     journal = {Electronic journal of differential equations},
     year = {2008},
     volume = {2008},
     zbl = {1137.35328},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a16/}
}
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%A Lin,  Yingzhen
%T Reproducing kernel methods for solving linear initial-boundary-value problems
%J Electronic journal of differential equations
%D 2008
%V 2008
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%F EJDE_2008__2008__a16
Yang,  Li-Hong; Lin,  Yingzhen. Reproducing kernel methods for solving linear initial-boundary-value problems. Electronic journal of differential equations, Tome 2008 (2008). http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a16/