A Review of Numerical Methods for Eigenvalue Problems Nonlinear in the Parameter

1977 ◽  
pp. 43-67 ◽  
Author(s):  
P. Lancaster
Keyword(s):  
Numerical Methods ◽  
Eigenvalue Problems

Numerical methods for the solution of special and general sixth-order boundary-value problems, with applications to Bénard layer eigenvalue problems

1990 ◽  
Vol 431 (1883) ◽  
pp. 433-450 ◽  
Keyword(s):  
Numerical Methods ◽  
Boundary Value Problems ◽  
Eigenvalue Problems ◽  
Boundary Value ◽  
Second Order ◽  
Sixth Order ◽  
Asymptotic Estimates ◽  
Eighth Order ◽  
The Family ◽  
Convergent Method

A family of numerical methods is developed for the solution of special nonlinear sixth-order boundary-value problems. Methods with second-, fourth-, sixth- and eighth-order convergence are contained in the family. The problem is also solved by writing the sixth-order differential equation as a system of three second-order differential equations. A family of second- and fourth-order convergent methods is then used to obtain the solution. A second-order convergent method is discussed for the numerical solution of general nonlinear sixth-order boundary-value problems. This method, with modifications where necessary, is applied to the sixth-order eigenvalue problems associated with the onset of instability in a Bénard layer. Numerical results are compared with asymptotic estimates appearing in the literature.

Numerical Methods for Eigenvalue Problems

2020 ◽  
pp. 287-298
Author(s):  
Federico Milano ◽  
Ioannis Dassios ◽  
Muyang Liu ◽  
Georgios Tzounas
Keyword(s):  
Numerical Methods ◽  
Eigenvalue Problems

A Chart of Numerical Methods for Structured Eigenvalue Problems

1992 ◽  
Vol 13 (2) ◽  
pp. 419-453 ◽  
Author(s):  
Angelika Bunse-Gerstner ◽  
Ralph Byers ◽  
Volker Mehrmann
Keyword(s):  
Numerical Methods ◽  
Eigenvalue Problems
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