Eigenvalue asymptotics for normalized Sturm-Liouville problems
Vander Meulen, David
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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.