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Constructive existence and uniqueness for some nonlinear two-point boundary value problems. (English) Zbl 0528.34018


MSC:

34B15 Nonlinear boundary value problems for ordinary differential equations
65L10 Numerical solution of boundary value problems involving ordinary differential equations

Citations:

Zbl 0172.195
Full Text: DOI

References:

[1] Aries, R., (The Mathematical Theory of Diffusion and Reaction on Permeable Catalysis, Vol. I (1975), Oxford Univ. Press (Clarendon): Oxford Univ. Press (Clarendon) London/New York) · Zbl 0315.76051
[2] DeSimone, J. A.; Pennline, J. A., A new asymptotic analysis of the \(n\) th order reaction-diffusion problem: Analytical and numerical studies, Math. Biosci., 40, 303-318 (1978) · Zbl 0397.92030
[3] Keller, H. B., Numerical Methods for Two-Point Boundary Value Problems, ((1968), Ginn (Blaisdell): Ginn (Blaisdell) Waltham, Mass), 106-127 · Zbl 0767.34014
[4] Pennline, J. A., Improving convergence rate in the method of successive approximations, Math. Comp., 37, 127-134 (1981) · Zbl 0475.65091
[5] Troesch, B. A., Intrinsic Difficulties in the Solution of a Boundary Value Problem, (Internal Rep. NN-142 (1960), TRW Inc: TRW Inc Redondo Beach, Calif) · Zbl 0442.76091
[6] Robert, S. M.; Shipman, J. S., Solution of Rroesch’s two-point boundary value problem by a combination of techniques, J. Comput. Phys., 10, 232-241 (1972) · Zbl 0247.65052
[7] Jones, D. J., Solutions of Troesch’s and other two-point boundary value problems by shooting techniques, J. Comput. Phys., 12, 429-434 (1973) · Zbl 0264.65046
[8] Kubecek, M.; Hlavacek, V., Solution of Troesch’s two-point boundary value problem by shooting techniques, J. Comput. Phys., 17, 95-101 (1975) · Zbl 0301.65047
[9] Chiou, J. P.; Na, T. Y., On the solution of Troesch’s nonlinear two-point boundary value problem using an initial value method, J. Comput. Phys., 19, 311-316 (1975) · Zbl 0318.65036
[10] Troesch, B. A., A simple approach to a sensitive two-point boundary value problem, J. Comput. Phys., 21, 279-290 (1976) · Zbl 0334.65063
[11] Roberts, S. M.; Shipman, J. S., On the closed form solution of Troesch’s problem, J. Comput. Phys., 21, 279-290 (1976) · Zbl 0334.65062
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