A shifted Jacobi polynomial collocation spectral algorithm for numerical solution of the coupled nonlinear time-fractional schr¨odinger equations

In this paper, an efficient and accurate collocation spectral numerical algorithm is presented for solving the nonlinear time-fractional coupled schr¨odinger partial differential equations with the initial, boundary and non-local conditions. The proposed algotithm has two steps. The first step depends on shifted Jacobi Gauss-Lobatto collocation (SJ-GL-C) method to transform the problem into a system of nonlinear fractional differential equations (NSFDEs) with initial conditions and the second step transforms the NSFDEs into a system of nonlinear algebraic equations by using shifted Jacobi Gauss-Radau collocation (SJ-GR-C) method. The numerical example confirms the efficientcy and accuracy of the method.