Eigenvalue inclusions for second-order ordinary differential operators by a numerical homotopy method
An automated homotopy method, based on elementary estimates, is described for the computation of inclusion intervals for the first N eigenvalues of Sturm-Liouville problems with either separated or periodic boundary conditions. Interval arithmetic (with FORTRAN-SC subroutines) is used to deal with roundoff. The method requires the solution of a number of related eigenvalue problems using approximations to the coefficients. Unlike some methods which require solution of a single problem with approximations to the coefficients [the reviewer, Congr. Numerantium 34, 3-16 (1982; Zbl 0535.65060)], the method is stated to be readily generalized to partial differential equations, and a paper on this is foreshadowed.
second-order ordinary differential operators
scientific article; zbMATH DE number 4162184
scientific article