Bibliography for Shooting Methods for ODE's

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  1. Infinitely Many Stationary Solutions for a Simple Climate Model via a Shooting Method
    Diaz, J. I.; Tello, L.
    Mathematical Methods in the Applied Sciences, 2002, vol. 25, no. 4, pp. 327-334, Ingenta.  
  2. Numerical results on alternating linear shooting method.    
    Kim, Do-Hyun; Lee, Sun-Woo    
    Far East J. Appl. Math. 5 (2001), no. 2, 211--223, MathSciNet.  
  3. 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.  
  4. 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.  
  5. Shooting method for non-linear vibration and thermal buckling of heated orthotropic circular plates
    Li, S.-R.; Zhou, Y.-H.
    Journal of Sound and Vibration, 2001, vol. 248, no. 2, pp. 379-386, Ingenta.  
  6. The shooting method for the solution of ordinary differential equations: a control-theoretical perspective
    Schaerer, C. E.; Kaszkurewicz, E.
    International Journal of Systems Science, 2001, vol. 32, no. 8, pp. 1047-1054, Ingenta.  
  7. Performance of Parallel Shooting Method for Closed Loop Guidance of an Optimal Launch Vehicle Trajectory
    Anand Jutty, K.; Bhat, M. S.; Ghose, D.
    Optimization and Engineering, 2000, vol. 1, no. 4, pp. 399-436, Ingenta.  
  8. Numerical Method of Parallel Shooting for Solving Multilayered Steady-State Boundary Problems in Membrane Electrochemistry.
    Lebedev, K.A.; Kovalev, I.V.
    Russian journal of electrochemistry, 1999, vol. 35, no. 10, pp. 1074, Ingenta.  
  9. Efficient shooting algorithms for solving the nonlinear one-dimensional scalar Helmholtz equation.   
    Jiménez, S.; Bulgakov, S.; Vázquez, L.    
    Appl. Math. Comput. 95 (1998), no. 2-3, 101--114, MathSciNet.  
  10. A shooting method for singular nonlinear second order Volterra integro-differential equations.   
    Shaw, R. E.; Garey, L. E.   
    International journal of mathematics and mathema, 1997, vol. 20, no. 3, pp. 589--598, MathSciNet.  
  11. Multiple shooting with dichotomically stable formulae for linear boundary-value problems.   
    Dueñas, E.; England, R.; López-Estrada, J.    
    Numerical mathematics and computational mechanics (Miskolc, 1996). Comput. Math. Appl. 38 (1999), no. 9-10, 143--159, MathSciNet.  
  12. 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.  
  13. Shooting methods for two-point BVPs with partially separated endconditions.   
    Hermann, M.; Kaiser, D.   
    Z. Angew. Math. Mech. 75 (1995), no. 9, 651--668, MathSciNet.  
  14. A Newton-Picard shooting method for computing periodic solutions of large-scale dynamical systems.
    Roose, D.; Lust, K.; Champneys, A.; Spence, A.
    Structure formation in continuous dynamical systems (Caputh, 1993). Chaos Solitons Fractals 5 (1995), no. 10, 1913--1925, MathSciNet.  
  15. Shooting methods for two-point BVPs with partially separated endconditions.
    Hermann, M.; Kaiser, D.
    Z. Angew. Math. Mech. 75 (1995), no. 9, 651--668, MathSciNet.  
  16. On numerical solution of the Schrodinger equation: the shooting method revisited.
    Indjin, D.; Todorovic, G.; Ikonic, Z.
    Computer physics communications, 1995, vol. 90, no. 1, pp. 87, Ingenta.  
  17. On a shooting algorithm for Sturm-Liouville eigenvalue problems with periodic and semi-periodic boundary conditions.    
    Ji, Xing Zhi    
    J. Comput. Phys. 111 (1994), no. 1, 74--80, MathSciNet.  
  18. 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.   
  19. 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.  
  20. 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.  
  21. Classical and vector Sturm-Liouville problems: recent advances in singular-point analysis and shooting-type algorithms.   
    Pryce, John D.    
    Proceedings of the Fifth International Congress on Computational and Applied Mathematics (Leuven, 1992). J. Comput. Appl. Math. 50 (1994), no. 1-3, 455--470, MathSciNet.  
  22. 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.   
  23. 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.  
  24. On shooting algorithm for Sturm-Liouville eigenvalue problems with periodic and semi-periodic boundary conditions.    
    Wong, Yau Shu; Ji, Xing Zhi    
    Appl. Math. Comput. 51 (1992), no. 2-3, 87--104, MathSciNet.  
  25. Parallel algorithms for initial value problems: parallel shooting.    
    Khalaf, B. M. S.; Hutchinson, D.    
    Parallel Comput. 18 (1992), no. 6, 661--673, MathSciNet.  
  26. 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.  
  27. Multiple shooting algorithms for jump-discontinuous problems in optimal control and estimation.    
    Mook, D. Joseph; Lew, Jiann-Shiun    
    IEEE Trans. Automat. Control 36 (1991), no. 8, 979--983, MathSciNet.  
  28. Global error estimates for the standard parallel shooting method.
    Marzulli, P.
    Journal of computational and applied mathematics, 1991, vol. 34, no. 2, pp. 233, Ingenta.  
  29. Pointwise and nodal error estimation in linear boundary value problems solved by the standard parallel shooting.    
    Gheri, G.    
    Approximation, optimization and computing, 81--83, North-Holland, Amsterdam, 1990, MathSciNet.  
  30. Asymptotic shooting method for the solution of differential equations.
    Holubec, A.; Stauffer, A. D.; Acacia, P.
    Journal of physics A, 1990, vol. 23, no. 18, pp. 4081, Ingenta.  
  31. On the theory of the multiple bilateral shooting method for linear problems with a boundary layer. (Russian)    
    Kuleshova, I. F.; Monastyrnyui, P. I.; Radaeva, V. A.    
    Dokl. Akad. Nauk BSSR 33 (1989), no. 2, 106--109, 187, MathSciNet.  
  32. Estimation of the global discretization error in shooting methods for linear boundary value problems.    
    Marzulli, P.; Gheri, G.    
    Proceedings of the 3rd International Congress on Computational and Applied Mathematics (Leuven, 1988). J. Comput. Appl. Math. 28 (1989), Special Issue, 309--314, MathSciNet.  
  33. 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.   
  34. 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.   
  35. Vectorisation of the multiple shooting method for the nonlinear boundary value problem in ordinary differential equations.
    Goldmann, Mark
    Parallel Comput. 7 (1988), no. 1, 97--110, MathSciNet.  
  36. The Existence of the Solution and the Globally Convergent Shooting Method for a Class of Two-Point Boundary Value Problems.
    Feng, Guo-chen
    Journal of computational mathematics, 1988, vol. 6, no. 3, pp. 282, Ingenta.  
  37. 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.  
  38. 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.   
  39. The combination of shooting methods and simplicial algorithms for the solution of boundary value problems (extended abstract).    
    Schilling, Klaus    
    XI symposium on operations research (Darmstadt, 1986), 425--426, Methods Oper. Res., 57, Athenäum/Hain/Hanstein, Königstein, 1987, MathSciNet.  
  40. 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.   
  41. 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.  
  42. 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.  
  43. 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.   
  44. Zur numerischen Behandlung von linearen Zweipunkt-Randwertproblemen mit Schießverfahren. (German) [On the numerical treatment of linear two-point boundary value problems with shooting methods]    
    Kaiser, D.    
    Proceedings of the fourth conference on numerical treatment of ordinary differential equations (Berlin, 1984), 89--99, Seminarberichte, 65, Humboldt Univ., Berlin, 1984, MathSciNet.  
  45. Estimating Regions of Existence of Unstable Periodic Orbits Using Computer-Based Techniques
    Ira Bruce Schwartz
    SIAM Journal on Numerical Analysis, Vol. 20, No. 1. (Feb., 1983), pp. 106-120.
  46. The numerical treatment of linear boundary value problems with partially separated boundary conditions by shooting methods.    
    Hermann, Martin; Kaiser, Dieter    
    Numerical treatment of differential equations, II (Jena, 1983), 91--145, Wissensch. Beitr., Friedrich-Schiller-Univ., Jena, 1984, MathSciNet.  
  47. 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.  
  48. Invariant imbedding and multiple shooting for the solution of unstable linear boundary value problems.    
    Breitenecker, F.    
    Appl. Math. Comput. 9 (1981), no. 4, 235--244, MathSciNet.  
  49. 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.  
  50. Improved shooting techniques for linear boundary value problems.    
    Garg, Vijay K.    
    Comput. Methods Appl. Mech. Engrg. 22 (1980), no. 1, 87--99, MathSciNet.  
  51. 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.   
  52. Projection Methods for Two-Point Boundary Value Problems  
    G. W. Reddien  
    SIAM Review, Vol. 22, No. 2. (Apr., 1980), pp. 156-171, Jstor.  
  53. 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.   
  54. 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.   
  55. 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.   
  56. 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.   
  57. 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.   
  58. 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.  
  59. 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.  
  60. Back-and-forth shooting method for solving two-point boundary-value problems.
    Orava, P. J.; Lautala, P. A. J.
    J. Optimization Theory Appl. 18 (1976), no. 4, 485--498, MathSciNet.  
  61. 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.
  62. 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.  
  63. 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.   
  64. 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.  
  65. "Shooting Technique" For Singular Perturbations  
    L. A. Skinner  
    SIAM Journal on Applied Mathematics, Vol. 25, No. 1. (Jul., 1973), pp. 28-31, Jstor.   
  66. On shooting methods for two-point boundary value problems.
    Bailey, Paul B.; Shampine, L. F.
    J. Math. Anal. Appl. 23 1968 235--249, MathSciNet.  

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2003