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Computing eigenvalues of periodic Sturm-Liouville problems using shooting technique and direct integration method. (English) Zbl 0913.65073
The authors study Sturm-Liouville eigenvalue problems of the form $(*)$ $-(p(t)y')'+ q(t)y= \lambda\cdot s(t)$, $y(0)= y(\pi)$, $y'(0)= y'(\pi)$ for $t\in [0,\omega]$ where $p'$, $q$, $s$ are real valued piecewise continuous and $\omega$-periodic functions; $p$, $s$ are positive in $[0,\omega]$. Equation $(*)$ is not reduced -- as usual -- into a system of differential equations of first order but is integrated directly by using shooting techniques. Five test problems show computational advantages comparing with methods reducing $(*)$ into a system of equations of the first order.
Reviewer: H.Ade (Mainz)

65L15Eigenvalue problems for ODE (numerical methods)
34L15Eigenvalues, estimation of eigenvalues, upper and lower bounds for OD operators
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