A method of lines for solving the nonlinear time- and space-fractional Schrödinger equation via stable Gaussian radial basis function interpolation

The stable Gaussian radial basis function (RBF) interpolation is applied to solve the time and space-fractional Schrödinger equation (TSFSE) in one and two-dimensional cases. In this regard, the fractional derivatives of stable Gaussian radial basis function interpolants are obtained. By a method of lines, the computations of the TSFSE are converted to a coupled system of Caputo fractional ODEs. To solve the resulting system of ODEs, a high-order finite difference method is proposed, and the computations are reduced to a coupled system of nonlinear algebraic equations, in each time step. Numerical illustrations are performed to certify the ability and accuracy of the new method. Some comparisons are made with the results in other literature.

کلیدواژه ها:

Caputo derivative ، Nonlinear ، Fractional Schrödinger equation ، Radial basis functions ، Riesz derivative