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