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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my-usm-ep.595352023-10-24T03:26:29Z B-Spline Collocation Methods For Coupled Nonlinear Schrödinger Equation 2021-01 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 http://eprints.usm.my/59535/ http://eprints.usm.my/59535/1/24%20Pages%20from%20HANIS%20SAFIRAH%20BINTI%20SAIFUL%20ANUAR-2.pdf application/pdf en public phd doctoral Perpustakaan Hamzah Sendut Pusat Pengajian Sains Matematik |
| institution |
Universiti Sains Malaysia |
| collection |
USM Institutional Repository |
| language |
English |
| topic |
QA1 Mathematics (General) |
| spellingShingle |
QA1 Mathematics (General) Saiful Anuar, Hanis Safirah Binti B-Spline Collocation Methods For Coupled Nonlinear Schrödinger Equation |
| 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. |
| format |
Thesis |
| qualification_name |
Doctor of Philosophy (PhD.) |
| qualification_level |
Doctorate |
| author |
Saiful Anuar, Hanis Safirah Binti |
| author_facet |
Saiful Anuar, Hanis Safirah Binti |
| author_sort |
Saiful Anuar, Hanis Safirah Binti |
| title |
B-Spline Collocation Methods For Coupled Nonlinear Schrödinger Equation |
| title_short |
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_sort |
b-spline collocation methods for coupled nonlinear schrödinger equation |
| granting_institution |
Perpustakaan Hamzah Sendut |
| granting_department |
Pusat Pengajian Sains Matematik |
| publishDate |
2021 |
| url |
http://eprints.usm.my/59535/1/24%20Pages%20from%20HANIS%20SAFIRAH%20BINTI%20SAIFUL%20ANUAR-2.pdf |
| _version_ |
1783729572413440000 |