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

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.

Keywords

• Hyperbolic equation
• linear initial-boundary conditions
• reproducing kernel space