Eighth-order magnetic moment of the electron. I. Second-order vertex containing second-, fourth-, and sixth-order vacuum polarization subdiagrams

1983 ◽  
Vol 27 (4) ◽  
pp. 867-876 ◽  
Author(s):  
T. Kinoshita ◽  
W. B. Lindquist
Keyword(s):  
Magnetic Moment ◽  
Vacuum Polarization ◽  
Second Order ◽  
Sixth Order ◽  
Eighth Order

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.

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