Matrix methods for the numerical solution of z J′ν (z) + HJν (z) = 0.

A matrix-theoretic approach for the numerical solution of z J′ν (z) + HJν (z) = 0, an equation of the classical boundary value problem, for z ≠ 0 given complex parameters H and ν, and for ν given H and z ≠ 0, is proposed and analyzed. In each case, the problem can be reformulated as an eigenvalue problem for an infinite complex symmetric tridiagonal matrix posed in the classical Hilbert space of all square-summable infinite sequences. The paper justifies the approximate solution by truncation, giving extremely accurate asymptotic error estimates. Computer experiments confirm the theoretical results. © 1997 Scripta Technica, Inc. Electron Comm Jpn Pt 3, 80(7): 44–54, 1997 [ABSTRACT FROM AUTHOR]