New, Fast Numerical Method for Solving Two-Point Boundary-Value Problems

Journal of Guidance, Control, and Dynamics

Volumn 27, Issue 2, 2004, Pages 301-304

  Holsapple, Raymond ^a,c   Venkataraman, Ram ^a,c   Doman, David ^b  

^a TEXAS TECH UNIVERSITY   (United States)

^b AIR FORCE RESEARCH LABORATORY   (United States)

^c Department of Mathematics ^*  (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; BOUNDARY CONDITIONS; CONTROL THEORY; DIFFERENTIAL EQUATIONS; FINITE DIFFERENCE METHOD; LINEAR SYSTEMS; MATRIX ALGEBRA; NONLINEAR SYSTEMS; NUMERICAL METHODS; OPTIMAL CONTROL SYSTEMS; PROBLEM SOLVING; THEOREM PROVING;

MULTIPLE-SHOOTING METHOD (MSM); NEWTON'S METHOD; SIMPLE-SHOOTING METHOD (SSM);

BOUNDARY VALUE PROBLEMS;

EID: 1842554869     PISSN: 07315090     EISSN: 15333884     Source Type: Journal    
DOI: 10.2514/1.1329     Document Type: Article

References (10)

1. Roberts, S. M., and Shipman, J. S., Two-Point Boundary Value Problems: Shooting Methods, Elsevier, New York, 1972, pp. 1-231.
2. Reinhardt, H.-J., Analysis of Approximation Methods for Differential and Integral Equations, Springer-Verlag, New York, 1985, pp. 72, 73.
3. Holsapple, R., Venkataraman, R., and Doman, D., "A Modified Simple Shooting Method for Solving Two Point Boundary Value Problems," Proceedings of the IEEE Aerospace Conference, Vol. 6, IEEE Press, New York, 2003, pp. 2783-2790.
4. Keller, H. 3., Numerical Methods for Two-Point Boundary-Value Problems, Blaisdell, Waltham, MA, 1968, pp. 7-18, 39-71.
5. Keller, H. B., Numerical Solution of Two Point Boundary Value Problems, CBMS-NSF Regional Conference Series in Applied Mathematics, Society for Industrial and Applied Mathematics, Philadelphia, 1976, pp. 1-19.
6. Morrison, D. D., Riley, J. D., and Zancanaro, J. F., "Multiple Shooting Method for Two-Point Boundary Value Problems," Communications of the ACM, Vol. 5, No. 12, 1962, pp. 613, 614.
7. Holt, J. F., "Numerical Solution of Nonlinear Two-Point Boundary Problems by Finite Difference Methods," Communications of the ACM, Vol. 7, No. 6, 1964, pp. 366-373.
8. Vinter, R., Optimal Control, Birkhäuser, Boston, MA, 2000, pp. 18-20, 91-108.
9. Stoer, J., and Bulirsch, R., Introduction to Numerical Analysis, 2nd ed., Springer-Verlag, New York, 1993, pp. 272-286, 502-535.
10. Shampine, L. F., Kierzenka, J., and Reichelt, M. W., Solving Boundary Value Problems for Ordinary Differential Equations in MATLAB with bvp4c, Mathworks Inc., Natick, MA, 2000, URL: ftp://ftp.mathworks.com/pub/doc/papers/bvp/[cited 26 Oct. 2000].