A nonlinear shooting method for two-point boundary value problems. (English) Zbl 0999.65077

Summary: We study a new nonlinear shooting method for solving two-point boundary value problems and show numerical experiments with various velocity conditions. We discuss and analyze the numerical solutions which are obtained by the shooting method.


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


[1] Bailey, P. B.; Shampine, L. F.; Waltman, P. E., Nonlinear Two Point Boundary Value Problems (1968), Academic Press: Academic Press New York · Zbl 0169.10502
[2] Roberts, S. M.; Shipman, J. S., Two Point Boundary Value Problems: Shooting Methods (1972), American Elsevier: American Elsevier New York · Zbl 0247.65052
[3] Burden, R. L.; Faires, J. D., Numerical Analysis (1993), PWS: PWS Boston · Zbl 0788.65001
[4] Greenspan, D.; Casulli, V., Numerical Analysis for Applied Mathematics, Science, and Engineering (1988), Addison-Wesley · Zbl 0658.65001
[5] Pohozaev, S. T., The Dirichlet problem for the equation Δ \(u = u^2\), Soviet Math., 1, 1143-1146 (1960) · Zbl 0097.08503
[6] Collatz, L., (The Numerical Treatment of Differential Equations (1960), Springer-Verlag: Springer-Verlag Heidelberg) · Zbl 0086.32601
[7] Keller, H. B., Numerical Methods for Two Point Boundary Value Problems (1968), Blaisdell: Blaisdell London · Zbl 0172.19503
[8] Nagle, R. K.; Saff, E. B., Fundamentals of Differential Equations and Boundary Value Problems (1993), Addison-Wesley: Addison-Wesley New York · Zbl 0773.34003
[9] Stakgold, I., Green’s Functions and Boundary Value Problems (1979), John Wiley & Sons: John Wiley & Sons New York · Zbl 0421.34027
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.