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.
Global extrapolation procedures on two and three grids, which increase the
order of convergence, are outlined.
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
