Abstract

Nonselfadjoint Boundary-Eigenvalue Problems L. Greenberg & M. Marletta This is a report on recent work with M. Marletta concerning eigenvalue approximation for nonselfadjoint problems of the form: y^{(n)}+ p_{n-1}(x)y^{(n-1} + \cdots + p_0(x)y = \lam w(x)y, together with $n$ boundary conditions. G.D. Birkhoff determined the asymptotic values of the eigenvalues for such problems which satisfy certain ``Birkhoff regularity'' conditions. We have shown that all even order problems with separated boundary conditions are Birkhoff regular. We have written a package of subroutines for even order problems with separated boundary conditions. The code can calculate the following: The eigenvalues in a rectangle; The eigenvalues in a left half-plane; The eigenvalues in a vertical strip; The $k^{th}$ eigenvalue as ordered by the real part. The code uses the argument principle. So far, we have subroutines for orders 2, 4, 6, and some vector-matrix problems. The code has been applied to the Orr-Sommerfeld problem.

General Enquiries Dr. Malcolm Brown. Computer Science Cardiff University PO Box 916 Cardiff CF24 3XF, U.K. Malcom@cs.cf.ac.uk

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