Electron. J. Diff. Eqns., Vol. 2008(2008), No. 29, pp. 1-11.

Reproducing kernel methods for solving linear initial-boundary-value problems

Li-Hong Yang, Yingzhen Lin

Abstract:
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.

Submitted January 26, 2008. Published February 28, 2008.
Math Subject Classifications: 35A35, 35A45, 35G05, 65N99.
Key Words: Hyperbolic equation; linear initial-boundary conditions; reproducing kernel space.

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Li-Hong Yang
College of Science, Harbin Engineering University
150001, China
email: lihongyang@hrbeu.edu.cn
  Yingzhen Lin
College of Science, Harbin Engineering University
150001, China
email: liliy55@163.com

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