A new high algebraic order efficient finite difference method for the solution of the Schrödinger equation

The development of a new five-stages symmetric two-step method of fourteenth algebraic order with vanished phase-lag and its first, second, third and fourth derivatives is analyzed in this paper. More specifically: (1) we will present the development of the new method, (2) we will determine the local truncation error (LTE) of the new proposed method, (3) we will analyze the local truncation error based on the radial time independent Schr?dinger equation, (4) we will study the stability and the interval of periodicity of the new proposed method based on a scalar test equation with frequency different than the frequency of the scalar test equation used for the phase-lag analysis, (5) we will test the efficiency of the new obtained method based on its application on the coupled differential equations arising from the Schr?dinger equation.

Hybrid high algebraic order two-step method with vanished phase-lag and its first, second, third, fourth and fifth derivatives

A hybrid tenth algebraic order two-step method with vanished phase-lag and its first, second, third, fourth and fifth derivatives are obtained in this paper. We will investigate • the construction of the method • the local truncation error (LTE) of the newly obtained method. We will also compare the lte of the newly developed method with other methods in the literature (this is called the comparative LTE analysis) • the stability (interval of periodicity) of the produced method using frequency for the scalar test equation different from the frequency used in the scalar test equation for phase-lag analysis (this is called stability analysis) • the application of the newly obtained method to the resonance problem of the Schrödinger equation. We will compare its effectiveness with the efficiency of other known methods in the literature. It will be proved that the developed method is effective for the approximate solution of the Schrödinger equation and related periodical or oscillatory initial value or boundary value problems.

An Efficient Numerical Method for the Solution of the Schrödinger Equation

The development of a new five-stage symmetric two-step fourteenth-algebraic order method with vanished phase-lag and its first, second, and third derivatives is presented in this paper for the first time in the literature. More specifically we will study(1)the development of the new method,(2)the determination of the local truncation error (LTE) of the new method,(3)the local truncation error analysis which will be based on test equation which is the radial time independent Schrödinger equation,(4)the stability and the interval of periodicity analysis of the new developed method which will be based on a scalar test equation with frequency different than the frequency of the scalar test equation used for the phase-lag analysis, and(5)the efficiency of the new obtained method based on its application to the coupled Schrödinger equations.