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Numerical methods of high-order accuracy for nonlinear boundary value problems. III: Eigenvalue problems, IV: Periodic boundary conditions. (English) Zbl 0181.18303

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[1] Birkhoff, G., C. de Boor, B. Swartz, andB. Wendroff: Rayleigh-Ritz approximation by piecewise cubic polynomials. SIAM J. Numer. Anal.3, 188–203 (1966). · Zbl 0143.38002 · doi:10.1137/0703015
[2] Brauer, Fred: Singular self-adjoint boundary value problems for the differential equationLx=\(\lambda\)Mx. Trans. Am. Math. Soc.88, 331–345 (1958). · Zbl 0141.27802
[3] Ciarlet, P. G., M. H. Schultz, andR. S. Varga: Numerical methods of highorder accuracy for nonlinear boundary value problems. I. One dimensional problem. Numer. Math.9, 394–430 (1967). · Zbl 0155.20403 · doi:10.1007/BF02162155
[4] –: Numerical methods of high-order accuracy for nonlinear boundary value problems. II. Nonlinear boundary conditions. Numer. Math.11, 331–345 (1968). · Zbl 0176.14901 · doi:10.1007/BF02166686
[5] Collatz, L.: The numerical treatment of differential equations, 3rd ed. (568 pp.). Berlin- Göttingen-Heidelberg: Springer 1960. · Zbl 0086.32601
[6] Courant, R.: Variational methods for the solution of problems of equilibrium and vibrations. Bull. Am. Math. Soc.49, 1–23 (1943). · Zbl 0063.00985 · doi:10.1090/S0002-9904-1943-07818-4
[7] –, andD. Hilbert: Methods of mathematical physics, vol. 1 (561 pp.). New York: Interscience Publishers, Inc. 1953
[8] Farrington, C. C., R. T. Gregory, andA. H. Taub: On the numerical solution of Sturm-Liouville differential equations. Math. Tables Aids Comput.11, 131–150 (1957). · Zbl 0083.12103 · doi:10.2307/2002075
[9] Gary, J.: Computing eigenvalues of ordinary differential equations by finite differences. Math. Comp.19, 365–379 (1965) · Zbl 0131.14302 · doi:10.1090/S0025-5718-1965-0179926-X
[10] Gould, S. H.: Variational methods for eigenvalue problems (275 pp.). Toronto: University of Toronto Press 1966. · Zbl 0156.12401
[11] Hardy, G. H., J. E. Littlewood, andG. Pólya: Inequalities, 2nd ed., (324 pp.). Cambridge: Cambridge University Press 1952. · Zbl 0047.05302
[12] Hubbard, B. E.: Bounds for eigenvalues of the Sturm-Liouville problem by finite difference methods. Arch. Rational Mech. Anal.10, 171–179 (1962). · Zbl 0196.49802 · doi:10.1007/BF00281184
[13] Kamke, E. A.: Über die definiten selbstadjungierten Eigenwertaufgaben bei gewöhnlichen linearen Differentialgleichungen. II, III. Math. Z.46, 231–286 (1940). · JFM 66.0416.03 · doi:10.1007/BF01181440
[14] –: Über die definiten selbstadjungierten Eigenwertaufgaben bei gewöhnlichen linearen Differentialgleichungen. IV. Math. Z.48, 67–100 (1942). · JFM 68.0197.01 · doi:10.1007/BF01180005
[15] Schultz, M. H., andR. S. Varga:L-splines. Numer. Math.10, 345–369 (1967). · Zbl 0183.44402 · doi:10.1007/BF02162033
[16] Weinberger, H. F.: Lower bounds for higher eigenvalues by finite difference methods. Pacific J. Math.8, 339–368 (1958). · Zbl 0084.34802 · doi:10.2140/pjm.1958.8.339
[17] Wendroff, B.: Bounds for eigenvalues of some differential operators by the Rayleigh-Ritz method. Math. Comp.19, 218–224 (1965). · Zbl 0139.10703 · doi:10.1090/S0025-5718-1965-0179932-5
[18] Yosida, K.: Functional analysis (458 pp.). New York: Academic Press 1965. · Zbl 0126.11504
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