Numerical solution of one-dimensional Sine--Gordon equation using Reproducing Kernel Hilbert Space Method
For researchers solving nonlinear partial differential equations, this is an incremental application of an existing method to a specific equation.
The paper applies the reproducing kernel Hilbert space method to solve the one-dimensional sine-Gordon equation, demonstrating accuracy through numerical examples compared to exact solutions and prior work.
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.