On the eigenvectors of a finite-difference approximation to the Sturm-Liouville eigenvalue problem
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- by Eckart Gekeler PDF
- Math. Comp. 28 (1974), 973-979 Request permission
Abstract:
This paper is concerned with a centered finite-difference approximation to to the nonselfadjoint Sturm-Liouville eigenvalue problem \[ \begin {array}{*{20}{c}} {L[u] = - {{[a(x){u_x}]}_x} - b(x){u_x} + c(x)u = \lambda u,\quad 0 < x < 1,} \hfill \\ {u(0) = u(1) = 0.} \hfill \\ \end {array} \] 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 $|{W_p}{|_2} = 1$.References
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Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Math. Comp. 28 (1974), 973-979
- MSC: Primary 65L15
- DOI: https://doi.org/10.1090/S0025-5718-1974-0356524-1
- MathSciNet review: 0356524