scholarly journals A new implicit symmetric method of sixth algebraic order with vanished phase-lag and its first derivative for solving Schrödinger's equation

2021 ◽  
Vol 19 (1) ◽  
pp. 225-237
Author(s):  
Saleem Obaidat ◽  
Rizwan Butt
Keyword(s):  
Phase Lag ◽  
Step Method ◽  
Method Performance ◽  
Schrödinger’S Equation ◽  
First Derivative ◽  
Algebraic Order ◽  
The One ◽  
Schrödinger's Equation ◽  
Better Than ◽  
Symmetric Method

Abstract In this article, we have developed an implicit symmetric four-step method of sixth algebraic order with vanished phase-lag and its first derivative. The error and stability analysis of this method are investigated, and its efficiency is tested by solving efficiently the one-dimensional time-independent Schrödinger’s equation. The method performance is compared with other methods in the literature. It is found that for this problem the new method performs better than the compared methods.

scholarly journals A New Explicit Four-Step Symmetric Method for Solving Schrödinger’s Equation

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1124 ◽  
Author(s):  
Saleem Obaidat ◽  
Said Mesloub
Keyword(s):  
Stability Analysis ◽  
Linear Method ◽  
Phase Lag ◽  
One Dimensional ◽  
Schrödinger’S Equation ◽  
First Derivative ◽  
Algebraic Order ◽  
The One ◽  
Schrödinger's Equation ◽  
Symmetric Method

In this article we have developed a new explicit four-step linear method of fourth algebraic order with vanished phase-lag and its first derivative. The efficiency of the method is tested by solving effectively the one-dimensional time independent Schrödinger’s equation. The error and stability analysis are studied. Also, the new method is compared with other methods in the literature. It is found that this method is more efficient than these methods.

A new efficient implicit four-step method with vanished phase-lag and some of its derivatives for the numerical solution of the radial Schr¨odinger equation

2017 ◽  
Vol 8 (1-2) ◽  
pp. 77 ◽  
Author(s):  
Ali Shokri ◽  
Morteza Tahmourasi
Keyword(s):  
Approximate Solution ◽  
Stability Analysis ◽  
Multistep Method ◽  
Phase Lag ◽  
Order Method ◽  
Step Method ◽  
One Dimensional ◽  
First Derivative ◽  
Algebraic Order ◽  
The One

A new four-step implicit linear sixth algebraic order method with vanished phase-lag and its first derivative is constructed in this paper. The purpose of this paper is to develop an efficient algorithm for the approximate solution of the one-dimensional radial Schr¨odinger equation and related problems. In order to produce an efficient multistep method the phase-lag property and its derivatives are used. An error analysis and a stability analysis is also investigated and a comparison with other methods is also studied. The efficiency of the new methodology is proved via theoretical analysis and numerical applications.

A SYMMETRIC HIGH ORDER METHOD WITH MINIMAL PHASE-LAG FOR THE NUMERICAL SOLUTION OF THE SCHRÖDINGER EQUATION

2001 ◽  
Vol 12 (07) ◽  
pp. 1035-1042 ◽  
Author(s):  
T. E. SIMOS ◽  
JESUS VIGO AGUIAR
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
New Method ◽  
Phase Lag ◽  
Step Method ◽  
High Order Method ◽  
Radial Schrödinger Equation ◽  
Algebraic Order ◽  
Minimal Phase ◽  
Symmetric Method

In this paper, a new high algebraic order symmetric eight-step method is introduced. For this method, a direct formula for the computation of the phase-lag is given. Based on this formula, an eight-step symmetric method with minimal phase-lag is developed. The new method has better stability properties than the classical one. Numerical illustrations on the radial Schrödinger equation indicate that the new method is more efficient than older ones.

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

2016 ◽  
Vol 27 (05) ◽  
pp. 1650049 ◽  
Author(s):  
Junyan Ma ◽  
T. E. Simos
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Truncation Error ◽  
Resonance Problem ◽  
Phase Lag ◽  
Step Method ◽  
Algebraic Order ◽  
Test Equation ◽  
The Stability ◽  
Scalar Test Equation

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.

scholarly journals On combined optical solitons of the one-dimensional Schrödinger’s equation with time dependent coefficients

Open Physics ◽  
2016 ◽  
Vol 14 (1) ◽  
pp. 65-68 ◽  
Author(s):  
Bulent Kilic ◽  
Mustafa Inc ◽  
Dumitru Baleanu
Keyword(s):  
Soliton Solutions ◽  
First Integral ◽  
Optical Solitons ◽  
Time Dependent ◽  
Ansatz Method ◽  
One Dimensional ◽  
Optical Metamaterials ◽  
Schrödinger’S Equation ◽  
The One ◽  
Schrödinger's Equation

AbstractThis paper integrates dispersive optical solitons in special optical metamaterials with a time dependent coefficient. We obtained some optical solitons of the aforementioned equation. It is shown that the examined dependent coefficients are affected by the velocity of the wave. The first integral method (FIM) and ansatz method are applied to reach the optical soliton solutions of the one-dimensional nonlinear Schrödinger’s equation (NLSE) with time dependent coefficients.

scholarly journals Bound State of Heavy Quarks Using a General Polynomial Potential

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Hesham Mansour ◽  
Ahmed Gamal
Keyword(s):  
Bound States ◽  
Bound State ◽  
Heavy Quarks ◽  
Polynomial Potential ◽  
Schrödinger’S Equation ◽  
General Polynomial ◽  
L Value ◽  
Schrödinger's Equation ◽  
Better Than ◽  
Good Agreement

In the present work, the mass spectra of the bound states of heavy quarks cc-,bb-, and Bc meson are studied within the framework of the nonrelativistic Schrödinger’s equation. First, we solve Schrödinger’s equation with a general polynomial potential by Nikiforov-Uvarov (NU) method. The energy eigenvalues for any L- value is presented for a special case of the potential. The results obtained are in good agreement with the experimental data and are better than previous theoretical studies.

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

Filomat ◽  
2017 ◽  
Vol 31 (15) ◽  
pp. 4999-5012 ◽  
Author(s):  
Ming Dong ◽  
Theodore Simos
Keyword(s):  
Truncation Error ◽  
Interval Of Periodicity ◽  
Phase Lag ◽  
Local Truncation Error ◽  
Step Method ◽  
Dinger Equation ◽  
Algebraic Order ◽  
Test Equation ◽  
The Stability ◽  
Scalar Test 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.

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