Document Details
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Document Type |
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Thesis |
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Document Title |
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NUMERICAL METHODS FOR COUPLED NONLINEAR SCHRODINGER EQUATIONS IN ONE , TWO AND THREE DIMENSIONS طرق عددية لمعادلات شرودنجر المزدوجة في بعد , بعدين وثلاثة أبعاد |
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Subject |
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Faculty of Sciences |
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Document Language |
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Arabic |
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Abstract |
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Numerical Methods for Coupled Nonlinear Schrödinger Equations in One, Two, and Three Dimensions By Suleman Hasan Alaseri Supervised by Prof. Mohammad Said Hammoudeh ABSTRACT The aim of this thesis is to solve numerically the coupled nonlinear Schrödinger equations (CNLSE) in one, two, and three dimensions. A new Alternating Direction Implicit (ADI) method, Linearized Alternating Direction Implicit (LADI) method, and time splitting method will be derived to do this job. The comparison between all these methods will be shown. In chapter 1: We write the general forms of the coupled nonlinear Schrödinger equations in one, two, and three dimensions, then we start to present in detail how to solve a block tridiagonal system by Crouts method. Also, we present Newtons method and fixed point method as two ways for solving nonlinear systems we obtained. In chapter 2: We study the coupled nonlinear Schrödinger equations in one dimension (1+1) using finite difference method and time splitting method. Each one of these methods will be done using Crank-Nicolson idea, which is second order in space and time, and Douglas idea, which is fourth order in space and second order in time. All of these schemes are unconditionally stable. Some examples will be given to show that all these methods are conserved the mass, momentum, and energy. The accuracy of all these methods are shown by comparison with the exact solution. In chapter 3: We study the coupled nonlinear Schrödinger equations in two dimensions (2+1) using ADI method, linearized ADI method, and time splitting method. Each one of these methods will be done using Crank-Nicolson idea, which is second order in space and time, and Douglas idea, which is fourth order in space and second order in time. All of these schemes are unconditionally stable. Some examples will be given to show that all of these methods are conserved. The accuracy of all these methods are sho |
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Supervisor |
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Prof. Mohammad Said Hammoudeh |
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Thesis Type |
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Doctorate Thesis |
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Publishing Year |
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1438 AH
2017 AD |
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Added Date |
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Friday, May 12, 2017 |
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Researchers
| سليمان حسن العسيري | Alaser, Suleman Hasan | Researcher | Doctorate | |
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