Bibliography for the Finite Difference Method for ODE's

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  1. 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.  
  2. A Finite-Difference Method for the Numerical Solution of the Sal'nikov Thermokinetic Oscillator Problem  
    U. S. Herges, E. H. Twizell  
    Proceedings: Mathematical and Physical Sciences, Vol. 449, No. 1936. (May 9, 1995), pp. 255-271, Jstor.  
  3. Finite Difference Method for Generalized Zakharov Equations  
    Qianshun Chang, Boling Guo, Hong Jiang  
    Mathematics of Computation, Vol. 64, No. 210. (Apr., 1995), pp. 537-553, Jstor.  
  4. Supplement to Finite Difference Method for Generalized Zakharov Equations  
    Qianshun Chang, Boling Guo, Hong Jiang  
    Mathematics of Computation, Vol. 64, No. 210. (Apr., 1995), pp. S7-S11, Jstor.  
  5. A Finite Difference Method for Symmetric Positive Differential Equations  
    Jinn-Liang Liu  
    Mathematics of Computation, Vol. 62, No. 205. (Jan., 1994), pp. 105-118, Jstor.  
  6. On Richardson extrapolation for finite difference methods on regular grids.  
    Fössmeier, Reinhard
    Numer. Math. 55 (1989), no. 4, 451--462, MathSciNet.  
  7. A Finite Difference Method for a Two-Sex Model of Population Dynamics  
    Todd Arbogast, Fabio A. Milner  
    SIAM Journal on Numerical Analysis, Vol. 26, No. 6. (Dec., 1989), pp. 1474-1486, Jstor.   
  8. 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.   
  9. 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.   
  10. 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.   
  11. 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.   
  12. Stability of Finite Difference Schemes for Two-Point Boundary Value Problems  
    C. De Boor, F. De Hoog  
    SIAM Journal on Numerical Analysis, Vol. 23, No. 5. (Oct., 1986), pp. 925-935, Jstor.  
  13. 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.  
  14. A Uniform Mesh Finite Difference Method for a Class of Singular Two-Point Boundary Value Problems  
    M. M. Chawla, C. P. Katti  
    SIAM Journal on Numerical Analysis, Vol. 22, No. 3. (Jun., 1985), pp. 561-565, Jstor.  
  15. Finite Difference Methods for Singular Two-Point Boundary Value Problems  
    E. J. Doedel, G. W. Reddien  
    SIAM Journal on Numerical Analysis, Vol. 21, No. 2. (Apr., 1984), pp. 300-313, Jstor.  
  16. 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.  
  17. A New Fourth-Order Finite-Difference Method for Solving Discrete-Ordinates Slab Transport Equations  
    Beny Neta, H. D. Victory, Jr.  
    SIAM Journal on Numerical Analysis, Vol. 20, No. 1. (Feb., 1983), pp. 94-105, Jstor.  
  18. 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.  
  19. Finite Element Methods of High-Order Accuracy for Singular Two-Point Boundary Value Problems with Nonsmooth Solutions  
    Robert Schreiber  
    SIAM Journal on Numerical Analysis, Vol. 17, No. 4. (Aug., 1980), pp. 547-566, Jstor.  
  20. Projection Methods for Two-Point Boundary Value Problems  
    G. W. Reddien  
    SIAM Review, Vol. 22, No. 2. (Apr., 1980), pp. 156-171, Jstor.  
  21. Finite Difference Collocation Methods for Nonlinear Two Point Boundary Value Problems  
    Eusebius J. Doedel  
    SIAM Journal on Numerical Analysis, Vol. 16, No. 2. (Apr., 1979), pp. 173-185, Jstor.  
  22. The Exact Order of Convergence for Finite Difference Approximations to Ordinary Boundary Value Problems  
    Wolf-Jurgen Beyn  
    Mathematics of Computation, Vol. 33, No. 148. (Oct., 1979), pp. 1213-1228, Jstor.  
  23. The Construction of Finite Difference Approximations to Ordinary Differential Equations  
    Eusebius J. Doedel  
    SIAM Journal on Numerical Analysis, Vol. 15, No. 3. (Jun., 1978), pp. 450-465, Jstor.  
  24. A Variable Mesh Finite Difference Method for Solving a Class of Parabolic Differential Equations in one Space Variable  
    T. H. Chong  
    SIAM Journal on Numerical Analysis, Vol. 15, No. 4. (Aug., 1978), pp. 835-857, Jstor.  
  25. A Comparison of Collocation and Finite Differences for Two-Point Boundary Value Problems  
    Robert D. Russell  
    SIAM Journal on Numerical Analysis, Vol. 14, No. 1. (Mar., 1977), pp. 19-39, Jstor.  
  26. 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.   
  27. 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.  
  28. 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.  
  29. On the Relative Efficiency of Higher Order Collocation Methods for Solving Two-Point Boundary Value Problems  
    R. F. Sincovec  
    SIAM Journal on Numerical Analysis, Vol. 14, No. 1. (Mar., 1977), pp. 112-123, Jstor.  
  30. 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.  
  31. A Variable Order Finite Difference Method for Nonlinear Multipoint Boundary Value Problems  
    M. Lentini, V. Pereyra  
    Mathematics of Computation, Vol. 28, No. 128. (Oct., 1974), pp. 981-1003+s1-s19, Jstor.  
  32. Bifurcation in Difference Approximations to Two-Point Boundary Value Problems  
    Richard Weiss  
    Mathematics of Computation, Vol. 29, No. 131. (Jul., 1975), pp. 746-760, Jstor.   
  33. Accurate Difference Methods for Nonlinear Two-Point Boundary Value Problems  
    Herbert B. Keller  
    SIAM Journal on Numerical Analysis, Vol. 11, No. 2. (Apr., 1974), pp. 305-320, Jstor.  
  34. 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.   
  35. Theory of a Finite Difference Method on Irregular Networks  
    V. Girault  
    SIAM Journal on Numerical Analysis, Vol. 11, No. 2. (Apr., 1974), pp. 260-282, Jstor.  
  36. 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.  
  37. Monotone and Oscillation Matrices Applied to Finite Difference Approximations  
    Harvey S. Price  
    Mathematics of Computation, Vol. 22, No. 103. (Jul., 1968), pp. 489-516, Jstor.  
  38. Minimising Truncation Error in Finite Difference Approximations to Ordinary Differential Equations  
    M. R. Osborne  
    Mathematics of Computation, Vol. 21, No. 98. (Apr., 1967), pp. 133-145, Jstor.  
  39. A method for finite-difference approximation to ordinary differential equations.    
    Osborne, M. R.    
    Comput. J. 7 1964 58--65, MathSciNet.  

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2003