scholarly journals Numerical Solutions of the Eigenvalue Problems of Sturm-Liouville Type by Using Power Series Approximation about Regular-Singular Points

2000 ◽  
Vol 138 ◽  
pp. 747-749 ◽  
Author(s):  
Tadashi Yano ◽  
Yasuo Ezawa ◽  
Hiroshi Ezawa ◽  
Takeshi Wada
Keyword(s):  
Power Series ◽  
Eigenvalue Problems ◽  
Numerical Solutions ◽  
Singular Points ◽  
Liouville Type ◽  
Series Approximation ◽  
Sturm Liouville

A high-speed method for eigenvalue problems. IV. Sturm-Liouville-type differential equations

1996 ◽  
Vol 96 (2-3) ◽  
pp. 247-262 ◽  
Author(s):  
T. Yano ◽  
K. Kitani ◽  
H. Miyatake ◽  
M. Otsuka ◽  
S. Tomiyoshi ◽  
...  
Keyword(s):  
Differential Equations ◽  
High Speed ◽  
Eigenvalue Problems ◽  
Liouville Type ◽  
Sturm Liouville ◽  
Speed Method

The eigenvalue problem with interaction conditions at one interior singular point

Filomat ◽  
2017 ◽  
Vol 31 (17) ◽  
pp. 5411-5420 ◽  
Author(s):  
Oktay Mukhtarov ◽  
Kadriye Aydemir
Keyword(s):  
Singular Point ◽  
Eigenvalue Problem ◽  
Quantum Physics ◽  
Eigenvalue Problems ◽  
Physical Processes ◽  
Liouville Type ◽  
Vibrating String ◽  
Sturm Liouville ◽  
Transfer Problems ◽  
String Problems

Some physical processes, both classical physics and quantum physics reduced to eigenvalue problems for Sturm-Liouville equations. In the recent years there has been an increasing interest in discontinuous eigenvalue problems for various Sturm-Liouville type equations. Such problems are connected with heat transfer problems, vibrating string problems, diffraction problems and etc. In this study we shall investigate a class of two order eigenvalue problem with supplementary transmission conditions at one interior singular point. We give an operator-theoretic interpretation in suitable Hilbert space.

scholarly journals Numerical solution of fractional Sturm-Liouville equation in integral form

2014 ◽  
Vol 17 (2) ◽  
Author(s):  
Tomasz Blaszczyk ◽  
Mariusz Ciesielski
Keyword(s):  
Numerical Scheme ◽  
Numerical Solutions ◽  
Integral Form ◽  
Time Interval ◽  
Finite Time Interval ◽  
Liouville Type ◽  
Sturm Liouville ◽  
Fractional Differential ◽  
Derivatives Of ◽  
Fractional Equation

AbstractIn this paper a fractional differential equation of the Euler-Lagrange/Sturm-Liouville type is considered. The fractional equation with derivatives of order α ∈ (0, 1] in the finite time interval is transformed to the integral form. Next the numerical scheme is presented. In the final part of this paper examples of numerical solutions of this equation are shown. The convergence of the proposed method on the basis of numerical results is also discussed.

Indefinite Eigenvalue Problems with Several Singular Points and Turning Points

2001 ◽  
Vol 229 (1) ◽  
pp. 51-71 ◽  
Author(s):  
Walter Eberhard ◽  
Gerhard Freiling ◽  
Kerstin Wilcken-Stoeber
Keyword(s):  
Eigenvalue Problems ◽  
Turning Points ◽  
Singular Points

scholarly journals Perturbation of eigenvalues due to gaps in two-dimensional boundaries

2006 ◽  
Vol 463 (2079) ◽  
pp. 759-786 ◽  
Author(s):  
Anthony M.J Davis ◽  
Stefan G Llewellyn Smith
Keyword(s):  
Eigenvalue Problems ◽  
Numerical Solutions ◽  
Neumann Boundary ◽  
Diffusion Problem ◽  
Length Scale ◽  
Two Dimensional ◽  
Constructive Approach ◽  
Term Outcome ◽  
Long Term Outcome

Motivated by problems involving diffusion through small gaps, we revisit two-dimensional eigenvalue problems with localized perturbations to Neumann boundary conditions. We recover the known result that the gravest eigenvalue is O (|ln  ϵ | −1 ), where ϵ is the ratio of the size of the hole to the length-scale of the domain, and provide a simple and constructive approach for summing the inverse logarithm terms and obtaining further corrections. Comparisons with numerical solutions obtained for special geometries, both for the Dirichlet ‘patch problem’ where the perturbation to the boundary consists of a different boundary condition and for the gap problem, confirm that this approach is a simple way of obtaining an accurate value for the gravest eigenvalue and hence the long-term outcome of the underlying diffusion problem.

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