Spectral Approximation and Existence of Solutions for Differential Equations using of Reproducing kernel Hilbert Space Method

In this paper, a reproducing kernel with polynomial form is used for finding analytical and approximate solutions of a second-order PDEs 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:

Spectral Approximation , Existence of solutions , Differential Equations , Reproducing Kernel , Hilbert Space.