Geodesic
Reproducing kernel methods for solving linear initial-boundary-value problems
Electronic Journal of Differential Equations, Tome 2008 (2008).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 
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     author = {Yang, Li-Hong and Lin, Yingzhen},
     title = {Reproducing kernel methods for solving linear initial-boundary-value problems},
     journal = {Electronic Journal of Differential Equations},
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     volume = {2008},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a16/}
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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/