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