A finite-difference method for the numerical solution of the Schrödinger equation

A new hybrid two-step method with vanished phase-lag and its first and second derivatives for the numerical solution of the Schrödinger equation and related problems

“…Theorem 1 [21] and [24] The symmetric 2m-step method with characteristic equation given by (6) has phase-lag order q and phase-lag constant c given by:…”

“…-In [9][10][11][12][13][14] exponentially and trigonometrically fitted Runge-Kutta and Runge-Kutta Nyström methods are obtained. -Multistep phase-fitted methods and multistep methods with minimal phase-lag are developed in [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37]. -Symplectic integrators are studied in .…”

A New Algorithm for the Approximation of the Schrödinger Equation

“…[4], [5] We call phase-lag of an algorithm (2) with the related characteristic equation (7) the dominant term of the expression…”

“…Theorem 1. [4] In order to compute the order of the phase-lag t and the constant of the phase-lag c for an algorithm (2) with the related equation (7), we use the direct formula:…”

“…We mention here that in the literature the last decades there are several variable step procedures for the approximation of the solution for systems of Schrödinger type equations [1][2][3][4][5][6][7][8][9][10][11][12][13][14].…”