B-Spline Collocation Methods For Coupled Nonlinear Schrödinger Equation

Saiful Anuar, Hanis Safirah Binti (2021) B-Spline Collocation Methods For Coupled Nonlinear Schrödinger Equation. PhD thesis, Perpustakaan Hamzah Sendut.

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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.

Item Type: Thesis (PhD)
Subjects: Q Science > QA Mathematics > QA1 Mathematics (General)
Divisions: Pusat Pengajian Sains Matematik (School of Mathematical Sciences) > Thesis
Depositing User: Mr Hasmizar Mansor
Date Deposited: 24 Oct 2023 03:26
Last Modified: 24 Oct 2023 03:26
URI: http://eprints.usm.my/id/eprint/59535

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