Electronic Journal of Differential Equations,
Vol. 2008(2008), No. 29, pp. 1-11.

Title: Reproducing kernel methods for solving linear
       initial-boundary-value problems
 
Authors: Li-Hong Yang (Harbin Engineering Univ., China)
         Yingzhen Lin (Harbin Engineering Univ., China)

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.