Nonoscillation of Mathieu’s equation whose coefficient is a finite Fourier series approximating a square wave

Jitsuro Sugie

doi:10.1007/s00605-017-1049-7

Nonoscillation of Mathieu’s equation whose coefficient is a finite Fourier series approximating a square wave

Monatshefte für Mathematik ◽

10.1007/s00605-017-1049-7 ◽

2017 ◽

Vol 186 (4) ◽

pp. 721-743 ◽

Cited By ~ 1

Author(s):

Jitsuro Sugie

Keyword(s):

Fourier Series ◽

Square Wave ◽

Mathieu’S Equation

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Gibbs-Wilbraham Phenomenon in Square Wave Function

Journal of the Institute of Engineering ◽

10.3126/jie.v14i1.20086 ◽

2018 ◽

Vol 14 (1) ◽

pp. 206-215

Author(s):

Bhupendra Budha ◽

Man Bahadur Subedi

Keyword(s):

Wave Function ◽

Fourier Series ◽

Spline Interpolation ◽

Cubic Spline ◽

Cubic Spline Interpolation ◽

Smooth Curves ◽

Square Wave ◽

Mathematical Relation

The aim of this paper is to show the fluctuation on overshoots of particular term due to change in magnitude of discontinuity in the square wave function represented in Fourier series and also is to address the mathematical relation between those parameters. Along with that, some graphical plots of different terms are given to illustrate the results and to interpolate data with smooth curves using Cubic spline interpolation in MATLAB.Journal of the Institute of Engineering, 2018, 14(1): 206-215

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On certain expansions of the solutions of Mathieu'S differential equation

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100022192 ◽

1942 ◽

Vol 38 (1) ◽

pp. 28-33 ◽

Cited By ~ 2

Author(s):

A. Erdélyi

Keyword(s):

Differential Equation ◽

Fourier Series ◽

Periodic Solutions ◽

Mathieu Functions ◽

Mathieu’S Equation ◽

Image Position

1. There are several known types of expansions of Mathieu functions, i.e. mod 2π periodic solutions of Mathieu's equation ((9), chap. 19),The simplest expansion is the Fourier seriesAlmost equally well known are Heine's expansion ((4), p. 414; see also (5) and (6))and

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