Eigenvalue inclusions for second-order ordinary differential operators by a numerical homotopy method
Copyright policy )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.
- University of Cologne Germany
automated homotopy method, Interval and finite arithmetic, Interval arithmetic, eigenvalue, Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators, inclusion intervals, Numerical solution of eigenvalue problems involving ordinary differential equations, Sturm-Liouville problems, Global methods, including homotopy approaches to the numerical solution of nonlinear equations, second-order ordinary differential operators
automated homotopy method, Interval and finite arithmetic, Interval arithmetic, eigenvalue, Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators, inclusion intervals, Numerical solution of eigenvalue problems involving ordinary differential equations, Sturm-Liouville problems, Global methods, including homotopy approaches to the numerical solution of nonlinear equations, second-order ordinary differential operators
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