Bibliography for Shooting Methods for ODE's

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  1. An Alternative to the Shooting Method for a Certain Class of Boundary Value Problems  
    David A Sanchez,
    American Mathematical Monthly, Vol. 108, No. 6, 2001, pp. 552-555.  
  2. A nonlinear shooting method for two-point boundary value problems
    Ha, S. N.
    Computers and Mathematics With Applications, 2001, vol. 42, no. ER10-11, pp. 1411-1420, Ingenta.  
  3. A Motivational Example for the Numerical Solution of Two-Point Boundary-Value Problems (in Classroom Notes)  
    Stephen M. Alessandrini  
    SIAM Review, Vol. 37, No. 3. (Sep., 1995), pp. 423-427, Jstor.  
  4. Shooting Methods for One-Dimensional Diffusion-Absorption Problems  
    V. Martinez, A. Marquina, R. Donat  
    SIAM Journal on Numerical Analysis, Vol. 31, No. 2. (Apr., 1994), pp. 572-589, Jstor.   
  5. Multiple solutions of boundary value problems: an elementary approach via the shooting method.   
    Dinca, Gheorghe; Sanchez, Luis   
    NoDEA Nonlinear Differential Equations Appl. 1 (1994), no. 2, 163--178, MathSciNet.  
  6. On the Shooting Method for a Class of Two-Point Singular Nonlinear Boundary Value Problems.
    Elgindi, M.B.M.; Langer, R.W.
    International journal of computer mathematics, 1994, vol. 51, no. 1/2, pp. 107, Ingenta.  
  7. Application of Global Methods in Parallel Shooting   
    M. E. Kramer, R. M. M. Mattheij   
    SIAM Journal on Numerical Analysis, Vol. 30, No. 6. (Dec., 1993), pp. 1723-1739, Jstor.   
  8. Optimizing the numerical integration of initial value problems in shooting methods for linear boundary value problems.    
    Rández, L.    
    SIAM J. Sci. Comput. 14 (1993), no. 4, 860--871, MathSciNet.  
  9. Shooting methods for diffusion-absorption processes. (Spanish)   
    Martínez, V.; Marquina, A.   
    Proceedings of the XII Congress on Differential Equations and Applications/II Congress on Applied Mathematics (Spanish) (Oviedo, 1991), 245--250, Univ. Oviedo, Oviedo, 1991, MathSciNet.  
  10. Graded-Mesh Difference Schemes for Singularly Perturbed Two-Point Boundary Value Problems  
    Eugene C. Gartland, Jr.  
    Mathematics of Computation, Vol. 51, No. 184. (Oct., 1988), pp. 631-657, Jstor.   
  11. On the Numerical Integration of Nonlinear Two-Point Boundary Value Problems Using Iterated Deferred Corrections. Part 2: The Development and Analysis of Highly Stable Deferred Correction Formulae  
    J. R. Cash  
    SIAM Journal on Numerical Analysis, Vol. 25, No. 4. (Aug., 1988), pp. 862-882, Jstor.   
  12. Shooting algorithms for two-point BVPs.    
    Hermann, M.    
    Numerical treatment of differential equations (Halle, 1987), 74--83, Teubner-Texte Math., 104, Teubner, Leipzig, 1988, MathSciNet.  
  13. The Factorization Method for the Numerical Solution of Two Point Boundary Value Problems for Linear ODE's  
    I. Babuska, V. Majer  
    SIAM Journal on Numerical Analysis, Vol. 24, No. 6. (Dec., 1987), pp. 1301-1334, Jstor.   
  14. A Note on the Relationship Between Finite-Difference and Shooting Methods for ODE Eigenvalue Problems  
    Michael B. Porter, Edward L. Reiss  
    SIAM Journal on Numerical Analysis, Vol. 23, No. 5. (Oct., 1986), pp. 1034-1039, Jstor.   
  15. Numerical Methods for Stiff Two-Point Boundary Value Problems  
    Heinz-Otto Kreiss, N. K. Nichols, David L. Brown  
    SIAM Journal on Numerical Analysis, Vol. 23, No. 2. (Apr., 1986), pp. 325-368, Jstor.  
  16. The Close Relationships Between Methods for Solving Two-Point Boundary Value Problems  
    Marianela Lentini, Michael R. Osborne, Robert D. Russell  
    SIAM Journal on Numerical Analysis, Vol. 22, No. 2. (Apr., 1985), pp. 280-309, Jstor.  
  17. On Optimal Shooting Intervals  
    R. M. M. Mattheij, G. W. M. Staarink  
    Mathematics of Computation, Vol. 42, No. 165. (Jan., 1984), pp. 25-40, Jstor.   
  18. The Stability of One-Step Schemes for First-Order Two-Point Boundary Value Problems  
    C. de Boor, F. de Hoog, H. B. de Keller  
    SIAM Journal on Numerical Analysis, Vol. 20, No. 6. (Dec., 1983), pp. 1139-1146, Jstor.  
  19. A Posteriori Error Bounds for Two-Point Boundary Value Problems  
    Gershon Kedem  
    SIAM Journal on Numerical Analysis, Vol. 18, No. 3. (Jun., 1981), pp. 431-448, Jstor.  
  20. Improved shooting techniques for linear boundary value problems.    
    Garg, Vijay K.    
    Comput. Methods Appl. Mech. Engrg. 22 (1980), no. 1, 87--99, MathSciNet.  
  21. The Shooting Method for the Numerical Solution of a Class of Nonlinear Boundary Value Problems  
    A. Granas, R. B. Guenther, J. W. Lee  
    SIAM Journal on Numerical Analysis, Vol. 16, No. 5. (Oct., 1979), pp. 828-836, Jstor.   
  22. Projection Methods for Two-Point Boundary Value Problems  
    G. W. Reddien  
    SIAM Review, Vol. 22, No. 2. (Apr., 1980), pp. 156-171, Jstor.  
  23. An Algorithm that is Globally Convergent with Probability One for a Class of Nonlinear Two-Point Boundary Value Problems  
    Layne T. Watson  
    SIAM Journal on Numerical Analysis, Vol. 16, No. 3. (Jun., 1979), pp. 394-401, Jstor.   
  24. A Double Shooting Scheme for Certain Unstable and Singular Boundary Value Problems  
    Alvin Bayliss  
    Mathematics of Computation, Vol. 32, No. 141. (Jan., 1978), pp. 61-71, Jstor.   
  25. A Shooting Algorithm for the Best Least Squares Solution of Two-Point Boundary Value Problems  
    W. F. Langford  
    SIAM Journal on Numerical Analysis, Vol. 14, No. 3. (Jun., 1977), pp. 527-542, Jstor.   
  26. Computational Solution of Linear Two-Point Boundary Value Problems Via Orthonormalization  
    Melvin R. Scott, Herman A. Watts  
    SIAM Journal on Numerical Analysis, Vol. 14, No. 1. (Mar., 1977), pp. 40-70, Jstor.   
  27. A Two-Point Series Method for Two-Point Boundary Value Problems: Theoretical Foundation  
    Andrew M. Olson  
    SIAM Journal on Numerical Analysis, Vol. 14, No. 1. (Mar., 1977), pp. 2-18, Jstor.   
  28. A Numerical Method for Singular Two Point Boundary Value Problems  
    D. C. Brabston, H. B. Keller  
    SIAM Journal on Numerical Analysis, Vol. 14, No. 5. (Sep., 1977), pp. 779-791, Jstor.  
  29. Numerov's Method with Deferred Corrections for Two-Point Boundary-Value Problems  
    James W. Daniel, Andrew J. Martin  
    SIAM Journal on Numerical Analysis, Vol. 14, No. 6. (Dec., 1977), pp. 1033-1050, Jstor.  
  30. Orava, P. J.; Lautala, P. A. J.
    Back-and-forth shooting method for solving two-point boundary-value problems.
    J. Optimization Theory Appl. 18 (1976), no. 4, 485--498, MathSciNet.  
  31. A Unified View of Some Methods for Stiff Two-Point Boundary Value Problems  
    Karl G. Guderley  
    SIAM Review, Vol. 17, No. 3. (Jul., 1975), pp. 416-442.
  32. A Comparison of Global Methods for Linear Two-Point Boundary Value Problems  
    R. D. Russell, J. M. Varah  
    Mathematics of Computation, Vol. 29, No. 132. (Oct., 1975), pp. 1007-1019, Jstor.  
  33. Interval Analysis and Two-Point Boundary Value Problems  
    F. Aleixo Oliveira  
    SIAM Journal on Numerical Analysis, Vol. 11, No. 2. (Apr., 1974), pp. 382-391, Jstor.   
  34. A Comparison of Some Numerical Methods for Two-Point Boundary Value Problems  
    James M. Varah  
    Mathematics of Computation, Vol. 28, No. 127. (Jul., 1974), pp. 743-755, Jstor.  
  35. "Shooting Technique" For Singular Perturbations  
    L. A. Skinner  
    SIAM Journal on Applied Mathematics, Vol. 25, No. 1. (Jul., 1973), pp. 28-31, Jstor.   

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2003