Solving singular perturbation problem of second order ordinary differential equation using the method of matched asymptotic expansion (MMAE)

2015 ◽  
Author(s):  
Firdawati binti Mohamed ◽  
Mohamad Faisal bin Abd Karim
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Asymptotic Expansion ◽  
Singular Perturbation ◽  
Second Order ◽  
Singular Perturbation Problem ◽  
Matched Asymptotic Expansion ◽  
Order Ordinary Differential Equation ◽  
Perturbation Problem

scholarly journals On the Existence of Eigenmodes of Linear Quasi-Periodic Differential Equations and their Relation to the MHD Continuum

1982 ◽  
Vol 37 (8) ◽  
pp. 830-839 ◽  
Author(s):  
A. Salat
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Differential Equations ◽  
Infinite Sequence ◽  
Periodic Coefficient ◽  
Second Order ◽  
Order Ordinary Differential Equation ◽  
Magnetic Surfaces ◽  
Toroidal Geometry

The existence of quasi-periodic eigensolutions of a linear second order ordinary differential equation with quasi-periodic coefficient f{ω1t, ω2t) is investigated numerically and graphically. For sufficiently incommensurate frequencies ω1, ω2, a doubly indexed infinite sequence of eigenvalues and eigenmodes is obtained.The equation considered is a model for the magneto-hydrodynamic “continuum” in general toroidal geometry. The result suggests that continuum modes exist at least on sufficiently ir-rational magnetic surfaces

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