B-Spline Collocation Methods For Coupled Nonlinear Schrödinger Equation

In this study, the Coupled Nonlinear Schrödinger Equation (CNLSE) which models the propagation of light waves in optical fiber is solved using numerical methods namely Finite Difference Method (FDM) and B-Spline collocation methods. The equation was discretized in space and time. We propose the d...

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Main Author: Saiful Anuar, Hanis Safirah Binti
Format: Thesis
Language:English
Published: 2021
Subjects:
Online Access:http://eprints.usm.my/59535/1/24%20Pages%20from%20HANIS%20SAFIRAH%20BINTI%20SAIFUL%20ANUAR-2.pdf
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author Saiful Anuar, Hanis Safirah Binti
author_facet Saiful Anuar, Hanis Safirah Binti
author_sort Saiful Anuar, Hanis Safirah Binti
collection USM
description In this study, the Coupled Nonlinear Schrödinger Equation (CNLSE) which models the propagation of light waves in optical fiber is solved using numerical methods namely Finite Difference Method (FDM) and B-Spline collocation methods. The equation was discretized in space and time. We propose the discretization of the nonlinear terms in the CNLSE following the Taylor approach and a newly developed approach called Besse. The theta-weighted method is used to generalize the scheme whereby the Crank-Nicolson scheme (i.e θ = 0.5) is chosen. The time derivatives are discretized by forward difference approximation. For each approach, the space dimension is then discretized by five different collocation methods independently. The first method for Taylor approach is based on FDM whereby the space derivatives are replaced by central difference approximation.
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spelling usm.eprints-595352023-10-24T03:26:29Z http://eprints.usm.my/59535/ B-Spline Collocation Methods For Coupled Nonlinear Schrödinger Equation Saiful Anuar, Hanis Safirah Binti QA1 Mathematics (General) In this study, the Coupled Nonlinear Schrödinger Equation (CNLSE) which models the propagation of light waves in optical fiber is solved using numerical methods namely Finite Difference Method (FDM) and B-Spline collocation methods. The equation was discretized in space and time. We propose the discretization of the nonlinear terms in the CNLSE following the Taylor approach and a newly developed approach called Besse. The theta-weighted method is used to generalize the scheme whereby the Crank-Nicolson scheme (i.e θ = 0.5) is chosen. The time derivatives are discretized by forward difference approximation. For each approach, the space dimension is then discretized by five different collocation methods independently. The first method for Taylor approach is based on FDM whereby the space derivatives are replaced by central difference approximation. 2021-01 Thesis NonPeerReviewed application/pdf en http://eprints.usm.my/59535/1/24%20Pages%20from%20HANIS%20SAFIRAH%20BINTI%20SAIFUL%20ANUAR-2.pdf Saiful Anuar, Hanis Safirah Binti (2021) B-Spline Collocation Methods For Coupled Nonlinear Schrödinger Equation. PhD thesis, Perpustakaan Hamzah Sendut.
spellingShingle QA1 Mathematics (General)
Saiful Anuar, Hanis Safirah Binti
B-Spline Collocation Methods For Coupled Nonlinear Schrödinger Equation
title B-Spline Collocation Methods For Coupled Nonlinear Schrödinger Equation
title_full B-Spline Collocation Methods For Coupled Nonlinear Schrödinger Equation
title_fullStr B-Spline Collocation Methods For Coupled Nonlinear Schrödinger Equation
title_full_unstemmed B-Spline Collocation Methods For Coupled Nonlinear Schrödinger Equation
title_short B-Spline Collocation Methods For Coupled Nonlinear Schrödinger Equation
title_sort b spline collocation methods for coupled nonlinear schrodinger equation
topic QA1 Mathematics (General)
url http://eprints.usm.my/59535/1/24%20Pages%20from%20HANIS%20SAFIRAH%20BINTI%20SAIFUL%20ANUAR-2.pdf
work_keys_str_mv AT saifulanuarhanissafirahbinti bsplinecollocationmethodsforcouplednonlinearschrodingerequation