Oscillation Theory and Numerical Solution of Sixth Order Sturm-liouville Problems
نویسنده
چکیده
Following earlier work on fourth order problems, we develop a shooting method to approximate the eigenvalues of 6th order Sturm-Liouville problems using a spectral function N() which counts the number of eigenvalues less than. This requires anòscillation' count obtained from certain solutions of the diierential equation, and we develop explicit algorithms for obtaining the exact oscillation count when the coeecients in the diierential equation are piecewise constant. This work requires the use of a homotopy to simplify the problems under scrutiny. We also show that the Riccati-like variables in which the diierential equation is integrated (for reasons of stability) satisfy a linear system of diierential equations and we exploit this to integrate the equation by computing a matrix exponential.
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