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

A high-speed method for solving eigenvalue problems: use of the spline function in Milne's method

1990 ◽  
Vol 61 (3) ◽  
pp. 387-394 ◽  
Author(s):  
Toshiaki Yokota ◽  
Tadashi Yano ◽  
Masashi Otsuka ◽  
Shigeo Matsushima
Keyword(s):  
High Speed ◽  
Spline Function ◽  
Eigenvalue Problems ◽  
Speed Method

The calculation of the latent roots and vectors of matrices on the pilot model of the A.C.E.

1954 ◽  
Vol 50 (4) ◽  
pp. 536-566 ◽  
Author(s):  
J. H. Wilkinson
Keyword(s):  
Differential Equations ◽  
High Speed ◽  
Storage Capacity ◽  
Eigenvalue Problems ◽  
High Accuracy ◽  
Point Of View ◽  
Aircraft Industry ◽  
Pilot Model ◽  
Very High ◽  
Latent Roots

ABSTRACTThe problem of finding the latent roots and vectors of matrices has been treated in a number of papers ((2)–(7)) mainly from the point of view of desk computers. In this paper the problem is treated from the standpoint of users of high-speed automatic computers. In the first section a number of iterative processes are described and, in the second, the techniques developed for using these processes on the Pilot Model of the Automatic Computing Engine. It is shown that the methods give very high accuracy and can be used to deal with matrices of high orders even on a machine of very limited storage capacity. They have been used on numerous matrices of orders up to 60 mainly on problems arising in the aircraft industry and on eigenvalue problems for systems of ordinary differential equations.

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.

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