M.S. (Master of Science)
Department of Mathematical Sciences
Eigenvalues; Strum-Liouville equation; Asymptotic expansions
In this thesis, we obtain asymptotic formulas for eigenvalues associated with the Liouville Normal Form of the general Sturm-Liouville equation (pu')' + (λk — Q)u=0 on the interval [a, b]. The method used is based on an iterative procedure for solving the associated Riccati equation and then developing an asymptotic ex- 1 pansion of the solution in decending powers of λ^(1/2) as A —» ∞. The eigenvalue asymptotic formulas are then found using series reversion. Examples of this process are carried out by the symbolic manipulator package, MAPLE.
Vander Meulen, David, "Eigenvalue asymptotics for normalized Sturm-Liouville problems" (1992). Graduate Research Theses & Dissertations. 2820.
Northern Illinois University
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