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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=λ·s(t), y(0)=y(π), y ' (0)=y ' (π) for t[0,ω] where p ' , q, s are real valued piecewise continuous and ω-periodic functions; p, s are positive in [0,ω]. 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)
MSC:
65L15Eigenvalue problems for ODE (numerical methods)
34L15Eigenvalues, estimation of eigenvalues, upper and lower bounds for OD operators