Accession Number : ADA195250
Title : A Continuous Analogue of Sturm Sequences in the Context of Sturm-Liouville Equations. Revision.
Descriptive Note : Final rept.,
Corporate Author : MARYLAND UNIV COLLEGE PARK DEPT OF MATHEMATICS
Personal Author(s) : Greenberg, L ; Babuska, I
PDF Url : ADA195250
Report Date : Feb 1988
Pagination or Media Count : 61
Abstract : A shooting method is presented for finding the n sub th eigenvalue and eigenfunction of a Sturm-Liouville equation, in which the eigenvalue occurs nonlinearly. The method is verified in two ways: by applying the Sturm comparison and oscillation theorems to the continuous problem; and by applying Sturm sequences to a discretization. The method works for general (separated) boundary conditions, and provides an a-posteriori error estimate for the approximate eigenvalue. Analogues of the Sturm comparison, oscillation and separation theorems are proved for the discrete problem. A related method, which involves critical lengths in the invariant imbedding method, is shown to be incorrect for general boundary conditions.
Descriptors : *EIGENVALUES, *PARTIAL DIFFERENTIAL EQUATIONS, BOUNDARIES, EIGENVECTORS, OSCILLATION, SEPARATION, THEOREMS, SOLUTIONS(GENERAL), ALGORITHMS, OPERATORS(MATHEMATICS), NUMERICAL METHODS AND PROCEDURES
Subject Categories : Theoretical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE