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High order approximation to Sturm-Liouville eigenvalues. (English) Zbl 0298.65058

MSC:
65L10 Numerical solution of boundary value problems involving ordinary differential equations
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References:
[1] Birkhoff, G., Fix, G.: Accurate eigenvalue computations for elliptic problems. In Numerical Solution of Field Problems in Continuum Physics, G. Birkhoff and R. Varga, eds., American Mathematical Society, Providence, 1970, pp. 111-151 · Zbl 0231.65087
[2] Canosa, J., Gomes de Olivera, R.: A new method for the solution of the Schrodinger equation. J. Computational Phys.5, 188-207 (1970) · Zbl 0195.17302 · doi:10.1016/0021-9991(70)90059-8
[3] Collatz, L.: The Numerical Treatment of Differential Equations. Berlin: Springer 1966 · Zbl 0173.17702
[4] Davis, P., Rabinowitz, P.: Numerical Integration. Boston: Ginn-Blaisdell, 1967 · Zbl 0154.17802
[5] de Boor, C., Swartz, B.: Collocation at Gaussian points, SIAM J. Numer. Anal.10, 582-606 (1973) · Zbl 0232.65065 · doi:10.1137/0710052
[6] Gordon, R.: Quantum scattering using piecewise analytic solutions, in Methods in Computational Physics, Vol. 10. B. Adler, ed., New York: Academic Press 1971, pp. 81-109
[7] Pruess, S.: Estimating the eigenvalues of Sturm-Liouville problems by approximating the differential equation, SIAM J. Numer. Anal.,10, 55-68 (1973) · Zbl 0259.65078 · doi:10.1137/0710008
[8] Pruess, S.: Solving linear bundary value problems by approximating the coefficients. Math. Comp.27, 551-562 (1973) · Zbl 0293.65057 · doi:10.1090/S0025-5718-1973-0371100-1
[9] Pruess, S.: Higher order approximations to Sturm-Liouville eigenvalues. Technical Report No. 283, The University of New Mexico, Albuquerque, 1973 · Zbl 0259.65078
[10] Wilkinson, J.: The Algebraic Eigenvalue Problem. Oxford: Oxford University Press 1965 · Zbl 0258.65037
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