  In this paper, we propose a reproducing kernel Hilbert space method (RKHSM)
for solving the sine--Gordon (SG) equation with initial and boundary conditions
based on the reproducing kernel theory. Its exact solution is represented in
the form of series in the reproducing kernel Hilbert space. Some numerical
examples have been studied to demonstrate the accuracy of the present method.
The results obtained from the method are compared with the exact solutions and
the earlier works. Results of numerical examples show that the presented method
is simple and effective.
