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

Obaidat, S.; Mesloub, Said

doi:10.3390/math7111124

Cited by 5 publications

(2 citation statements)

References 32 publications

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“…Partial differential equations modelling dissipative processes usually involve complex coefficient functions or complex boundary conditions [6]. Other applications leading to complex linear systems include the discretization of time-dependent Schrödinger equations with implicit differential equations [7][8][9], inverse scattering problems, underwater acoustics, eddy current calculations [10], diffuse optical tomography [11], numerical calculations in quantum chromodynamics and numerical conformal mapping [12]. There are several methods to solve complex systems of linear equations.…”

Section: Introductionmentioning

confidence: 99%

ABS-Based Direct Method for Solving Complex Systems of Linear Equations

Abaffy

Fodor

2021

Mathematics

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Efficient solution of linear systems of equations is one of the central topics of numerical computation. Linear systems with complex coefficients arise from various physics and quantum chemistry problems. In this paper, we propose a novel ABS-based algorithm, which is able to solve complex systems of linear equations. Theoretical analysis is given to highlight the basic features of our new algorithm. Four variants of our algorithm were also implemented and intensively tested on randomly generated full and sparse matrices and real-life problems. The results of numerical experiments reveal that our ABS-based algorithm is able to compute the solution with high accuracy. The performance of our algorithm was compared with a commercially available software, Matlab’s mldivide (\) algorithm. Our algorithm outperformed the Matlab algorithm in most cases in terms of computational accuracy. These results expand the practical usefulness of our algorithm.

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Section: Introductionmentioning

confidence: 99%

ABS-Based Direct Method for Solving Complex Systems of Linear Equations

Abaffy

Fodor

2021

Mathematics

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“…The analytical solution of the NLS with varying coefficients has attracted great interest in the recent past (e.g., see [5][6][7] or more recent works in [8][9][10][11] and references therein). Additionally, the computation of the NLS is a critical part of the verification process of the analytical theories.…”

Section: Introductionmentioning

confidence: 99%

Efficient Computation of the Nonlinear Schrödinger Equation with Time-Dependent Coefficients

et al. 2020

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Motivated by the limited work performed on the development of computational techniques for solving the nonlinear Schrödinger equation with time-dependent coefficients, we develop a modified Runge-Kutta pair with improved periodicity and stability characteristics. Additionally, we develop a modified step size control algorithm, which increases the efficiency of our pair and all other pairs included in the numerical experiments. The numerical results on the nonlinear Schrödinger equation with a periodic solution verified the superiority of the new algorithm in terms of efficiency.The new method also presents a good behaviour of the maximum absolute error and the global norm in time, even after a high number of oscillations.

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

Obaidat

Butt

2021

Open Mathematics

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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.

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

Cited by 5 publications

References 32 publications

ABS-Based Direct Method for Solving Complex Systems of Linear Equations

ABS-Based Direct Method for Solving Complex Systems of Linear Equations

Efficient Computation of the Nonlinear Schrödinger Equation with Time-Dependent Coefficients

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

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