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

Numerical solution of one-dimensional Sine--Gordon equation using Reproducing Kernel Hilbert Space Method