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Mathematics of Computation

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On the eigenvectors of a finite-difference approximation to the Sturm-Liouville eigenvalue problem


Author: Eckart Gekeler
Journal: Math. Comp. 28 (1974), 973-979
MSC: Primary 65L15
MathSciNet review: 0356524
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Abstract: This paper is concerned with a centered finite-difference approximation to to the nonselfadjoint Sturm-Liouville eigenvalue problem

\begin{displaymath}\begin{array}{*{20}{c}} {L[u] = - {{[a(x){u_x}]}_x} - b(x){u_... ...0 < x < 1,} \hfill \\ {u(0) = u(1) = 0.} \hfill \\ \end{array} \end{displaymath}

It is shown that the eigenvectors $ {W_p}$ of the $ M \times M$-matrix ( $ \Delta x = 1/(M + 1)$ mesh size), which approximates L, are bounded in the maximum norm independent of M if they are normalized so that $ \vert{W_p}{\vert _2} = 1$.

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DOI: https://doi.org/10.1090/S0025-5718-1974-0356524-1
Keywords: Sturm-Liouville eigenvalue problem, finite-difference approximation
Article copyright: © Copyright 1974 American Mathematical Society