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


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


[1] {\scM. 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] {\scJ.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.{\bf19}, 311-316 · Zbl 0318.65036
[5] Firnett, P.J.; Troesch, B.A., Shooting-splitting method for sensitive two-point boundary value problems, (), 408-433 · Zbl 0282.65064
[6] Henrici, P., Discrete variable methods in ordinary differential equations, (1962), Wiley New York · Zbl 0112.34901
[7] Jones, D.J., J. computational phys., 12, 429-434, (1973)
[8] {\scM. Kubiček and V. Hlaváček}, Solution of Troesch’s two-point boundary value problem by shooting technique, J. Computational Phys.{\bf17}, 95-101 · Zbl 0301.65047
[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., (), 114, Heidelberger-Taschenbuch 114, Chap. VII
[13] Troesch, B.A., Intrinsic difficulties in the numerical solution of a boundary value problem, () · Zbl 0442.76091
[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, (), 96 · Zbl 0173.44403
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.