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Numerische Behandlung von Verzweigunsproblemen bei gewöhnlichen Differentialgleichungen. (German) Zbl 0413.65064

MSC:
65L15 Numerical solution of eigenvalue problems involving ordinary differential equations
65L10 Numerical solution of boundary value problems involving ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
34L99 Ordinary differential operators
74G60 Bifurcation and buckling
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References:
[1] Crandall, M.G., Rabinowitz, P.H.: Bifurcation from Simple Eigenvalues. Journal Functional Analysis8, 321-340 (1971) · Zbl 0219.46015 · doi:10.1016/0022-1236(71)90015-2
[2] Crandall, M.G., Rabinowitz, P.H.: Bifurcation, Perturbation of Simple Eigenvalues and Linearized Stability. Arch. Rational Mech. Anal.52, 161-180 (1973) · Zbl 0275.47044 · doi:10.1007/BF00282325
[3] Keener, J.P., Keller, H.B.: Perturbed Bifurcation Theory. Arch. Rational Mech. Anal.50, 159-175 (1973) · Zbl 0254.47080 · doi:10.1007/BF00703966
[4] Keller, H.B., Langford, W.F.: Iterations, Perturbations and Multiplicities for Nonlinear Bifurcation Problems. Arch. Rational Mech. Anal.48, 83-108 (1972) · Zbl 0249.47058 · doi:10.1007/BF00250427
[5] Langford, W.F.: Numerical Solution of Bifurcation Problems for Ordinary Differential Equations. Numer. Math.28, 171-190 (1977) · Zbl 0344.65042 · doi:10.1007/BF01394451
[6] Reid, W.T.: Generalized Greens’ Matrices for Two-Point Boundary Problems, SIAM J. Appl. Math.15, 856-870 (1967) · Zbl 0157.15304 · doi:10.1137/0115074
[7] Reid, W.T.: Ordinary Differential Equations, New York: Wiley & Sons, 1971 · Zbl 0212.10901
[8] Seydel, R.: Numerische Berechnung von Verzweigungen bei gewöhnlichen Differentialgleichungen, TUM-MATH-7736. Technische Universität München, 1977
[9] Simpson, R.B.: Finite Difference Methods for Mildly Nonlinear Eigenvalue Problems. SIAM J. Numer. Anal.8, 190-211 (1971) · Zbl 0232.65078 · doi:10.1137/0708021
[10] Weber, H.: A-posteriori-Fehlerabschätzungen und-Existenzaussagen bei der Lösung von gewöhnlichen Randwertaufgaben mit einem Differenzenverfahren. ZAMM57, T 310-312 (1977) · Zbl 0355.65058
[11] Weiss, R.: Bifurcation in Difference Approximations to Two-Point Boundary Value Problems. Math. Comp.29, 746-760 (1975) · Zbl 0327.65063 · doi:10.1090/S0025-5718-1975-0383763-7
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