STURM'S THEOREM AND THE ZEROS OF A SOLUTION TO A DIFFERENTIAL EQUATION
Abstract
The number of zeros contained in a given interval (a,b) for a solution to a Sturm-Liouville differential equation is of importance in many problems of mathematical physics. This number may be determined through Sturm's Comparison Theorem. Given one zero of the solution to a Sturm-Liouville differential equation, a technique, based upon Sturm's Theorem, of computing the next consecutive zero of the solution is proposed. The existence of a function which satisfies the desired end results of the proposed technique is shown. The technique is then applied to Bessel's differential equation and the results tabulated for the first 20 roots of the zeros of the Bessel function of order zero and one. Unfortunately this technique did not achieve the desired result of convergence to successive zeros of the given Bessel Function.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1963
- Accession Number
- AD0482300
Entities
People
- William A. Overbay
Organizations
- Naval Postgraduate School