electrochemical_55854

fractional

radical polymerization

schemes

conjugated polymer

suicides

discrete

fractional diffusion

iron oxide nanoparticles

tourism hospitality

mi mi_99852

hebbian

fully discrete

chips

caputo fractional derivative

error_117031

water wave

klein-gordon

Journal of Computational Physics

In this paper, a fast linearized conservative finite element method is studied for solving the strongly coupled nonlinear fractional Schrödinger equations. We prove that the scheme preserves both the mass and energy, which are defined by virtue of some recursion relationships. Using the Sobolev inequalities and then employing the mathematical induction, the discrete scheme is proved to be unconditionally convergent in the sense of L 2 -norm and H α / 2 -norm, which means that there are no any constraints on the grid ratios. Then, the prior bound of the discrete solution in L 2 -norm and L ∞ -norm are also obtained. Moreover, we propose an iterative algorithm, by which the coefficient matrix is independent of the time level, and thus it leads to Toeplitz-like linear systems that can be efficiently solved by Krylov subspace solvers with circulant preconditioners. This method can reduce the memory requirement of the proposed linearized finite element scheme from O ( M 2 ) to O ( M ) and the computational complexity from O ( M 3 ) to O ( M log ⁡ M ) in each iterative step, where M is the number of grid nodes. Finally, numerical results are carried out to verify the correction of the theoretical analysis, simulate the collision of two solitary waves , and show the utility of the fast numerical solution techniques.

A fast linearized conservative finite element method for the strongly coupled nonlinear fractional Schrödinger equations