A pseudospectral Sinc method for numerical investigation of the nonlinear time-fractional Klein-Gordon and sine-Gordon equations

In this paper, a pseudospectral method is proposed for solving the nonlinear time-fractional Klein-Gordon and sine-Gordon equations. The method is based on the Sinc operational matrices. A finite difference scheme is used to discretize the Caputo time-fractional derivative, while the spatial derivatives are approximated by the Sinc method. The convergence of the full discretization of the problem is studied. Some numerical examples are presented to confirm the accuracy and efficiency of the proposed method. The numerical results are compared with the analytical solution and the reported results in the literature.

Keywords:

fractional differential equation , Nonlinear Klein-Gordon and sine-Gordon equations , Sinc operational matrices , Pseudospectral method , Convergence