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On the closed form solution of Troesch’s problem. (English) Zbl 0334.65062

MSC:
65L10Boundary value problems for ODE (numerical methods)
34B15Nonlinear boundary value problems for ODE
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Full Text: DOI
References:
[1] M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, U.S. Dept. of Commerce, National Bureau of Standards, Applied Mathematics Series 55. · Zbl 0171.38503
[2] Bulirsch, R.: Die mehrzielmethode zur numerischen lösung von nichtlinearen randwertproblemen und aufgaben der optimalen steuerung. Vortrag im lehrgang flugbahnoptimierung der carl cranz-gesellschaft E. V. (October 1971)
[3] Bulirsch, R.; Stoer, J.: Numer. math.. 8, 1-13 (1966)
[4] J.P. Chiou and T.Y. Na, On the solution of Troesch’s nonlinear two-point boundary value problem using an initial value method, J. Computational Phys. 19, 311--316 · Zbl 0318.65036
[5] Firnett, P. J.; Troesch, B. A.: Shooting-splitting method for sensitive two-point boundary value problems. Lecture notes in mathematics 362, 408-433 (1974) · Zbl 0282.65064
[6] Henrici, P.: Discrete variable methods in ordinary differential equations. (1962) · Zbl 0112.34901
[7] Jones, D. J.: J. computational phys.. 12, 429-434 (1973)
[8] M. Kubiček and V. Hlaváček, Solution of Troesch’s two-point boundary value problem by shooting technique, J. Computational Phys. 17, 95--101
[9] Miele, A.; Aggarwal, A. K.; Tietze, J. L.: J. computational phys.. 15, 117-133 (1974)
[10] Roberts, S. M.; Shipman, J. S.: J. computational phys.. 10, 232-241 (1972)
[11] Stakgold, I.: SIAM rev.. 13, 289-332 (1971)
[12] Stoer, J.; Bulmscii, R.: 2nd ed. Einfuhrung in die numerische matematik. Einfuhrung in die numerische matematik, 114 (1973)
[13] Troesch, B. A.: Intrinsic difficulties in the numerical solution of a boundary value problem. Internal report NN-142 (January 29, 1960)
[14] Tsuda, Y.; Ichada, K.; Kryono, T.: Numer. math.. 10, 110-116 (1967)
[15] Gear, C. W.: Numerical initial value problems in ordinary differential equations. Subroutine DIFSUB, 96 (1971) · Zbl 1145.65316