Reproducing kernel methods for solving linear initial-boundary-value problems. (English) Zbl 1137.35328

Yang, Li-Hong; Lin, Yingzhen

Electron. J. Differ. Equ. 2008, Paper No. 29, 11 p. (2008).

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.

MSC:

35C10	Series solutions to PDEs
35A35	Theoretical approximation in context of PDEs
65N99	Numerical methods for partial differential equations, boundary value problems

Keywords:

Hyperbolic equation; reproducing kernel space; kernel with polynomial form