1. Twin solutions of boundary value problems for ordinary differential equations and finite difference equations.    
   Avery, R. I.; Chyan, Chuan Jen; Henderson, J.    
   Advances in difference equations, III. Comput. Math. Appl. 42 (2001), no. 3-5, 695--704, MathSciNet.  
2. Convergence analysis of finite difference approximations on equidistributed grids to a singularly perturbed boundary value problem.
   Beckett, G.; Mackenzie, J. A.
   Appl. Numer. Math. 35 (2000), no. 2, 87--109, MathSciNet.  
3. On invariant manifolds of finite difference methods for second-order ordinary differential equations. (Russian)    
   Fishman, L. Z.    
   Dokl. Akad. Nauk 364 (1999), no. 4, 455--456, MathSciNet.  
4. Continuous finite difference approximations for solving differential equations.
   Onumanyi, P.; Sirisena, U. W.; Jator, S. N.
   S. O. Fatunla commemorative. Int. J. Comput. Math. 72 (1999), no. 1, 15--27, MathSciNet.  
5. The variational equation for finite difference equations.
   Sánchez, David A.
   Dynam. Contin. Discrete Impuls. Systems 6 (1999), no. 3, 459--464, MathSciNet.  
6. A finite difference method for dispersive linear waves with applications to simulating microwave pulses in water.
   Luke, Jonathan H. C.
   J. Comput. Phys. 148 (1999), no. 1, 199--226, MathSciNet.  
7. On the solution by fourth order finite difference method for certain singular boundary value problems.
   Sen, Rabindra Nath; Hossain, Md. Bellal
   Soochow J. Math. 23 (1997), no. 3, 253--275, MathSciNet.  
8. Nonstandard finite difference equations for ODEs and 1-D PDEs based on piecewise linearization.
   Ramos, J. I.; García-López, C. M.
   Appl. Math. Comput. 86 (1997), no. 1, 11--36, MathSciNet.  
9. Explicit finite-difference methods for non-linear dynamic systems: Froude's pendulum.
   Djidjeli, K.; Guan, Z.; Price, W. G.; Twizell, E. H.
   Comput. Methods Appl. Mech. Engrg. 135 (1996), no. 3-4, 243--264, MathSciNet.  
10. 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.  
11. 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.  
12. 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.  
13. 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.  
14. 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.  
15. Finite-difference methods for solving the reaction-diffusion equations of a simple isothermal chemical system.
    Twizell, E. H.; Wang, Yigong; Price, W. G.; Fakhr, F.
    Numer. Methods Partial Differential Equations 10 (1994), no. 4, 435--454, MathSciNet.  
16. Sharp error estimates for the numerical solution of boundary value problems of ordinary differential equations by finite difference schemes.    
    Büttgenbach, B.; Esser, H.; Nessel, R. J.    
    Atti Sem. Mat. Fis. Univ. Modena 41 (1993), no. 2, 417--429, MathSciNet.  
17. On the comparison of error bounds for finite difference schemes.
    Büttgenbach, B.; Esser, H.; Nessel, R. J.
    Numer. Math. 64 (1993), no. 4, 477--486, MathSciNet.  
18. Five-diagonal finite difference methods based on mixed-type interpolation for a certain fourth-order two-point boundary-value problem.
    Van Daele, M.; Vanden Berghe, G.; De Meyer, H.
    Comput. Math. Appl. 24 (1992), no. 10, 55--76, MathSciNet.  
19. On the sharpness of error bounds in connection with finite difference schemes on uniform grids for boundary value problems of ordinary differential equations.    
    Büttgenbach, B.; Esser, H.; Nessel, R. J.    
    Numer. Funct. Anal. Optim. 12 (1991), no. 3-4, 285--298, MathSciNet.  
20. Finite-difference models of ordinary differential equations: influence of denominator functions.    
    Mickens, Ronald E.; Smith, Arthur    
    J. Franklin Inst. 327 (1990), no. 1, 143--149, MathSciNet.  
21. On Richardson extrapolation for finite difference methods on regular grids.  
    Fössmeier, Reinhard
    Numer. Math. 55 (1989), no. 4, 451--462, MathSciNet.  
22. 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.   
23. 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.   
24. The algebraic theory approach for ordinary differential equations: highly accurate finite differences.    
    Herrera, Ismael    
    Numer. Methods Partial Differential Equations 3 (1987), no. 3, 199--218, MathSciNet.  
25. Stability analysis of finite difference, pseudospectral and Fourier-Galerkin approximations for time-dependent problems.
    Tadmor, Eitan
    SIAM Rev. 29 (1987), no. 4, 525--555, MathSciNet.  
26. 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.   
27. 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.   
28. 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.   
29. 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.  
30. 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.  
31. 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.  
32. An overview of the treatment of ordinary differential equations by finite differences.    
    Herrera, Ismael; Chargoy, Lucía    
    Mathematical modelling in science and technology (Berkeley, Calif., 1985). Math. Modelling 8 (1987), 17--19, MathSciNet.  
33. Unified approach to numerical methods. III. Finite differences and ordinary differential equations.    
    Herrera, Ismael; Chargoy, Lucía; Alduncin, Gonzalo    
    Numer. Methods Partial Differential Equations 1 (1985), no. 4, 241--258, MathSciNet.  
34. Convergence of finite difference solutions of a class of boundary value problems for ordinary differential equations. (Chinese)    
    Zheng, Dao Sheng; Huang, Li Ping    
    J. East China Norm. Univ. Natur. Sci. Ed. 1985, no. 3, 20--28, MathSciNet.  
35. Finite difference solution of boundary value problems in ordinary differential equations.    
    Pereyra, V.   
    Studies in numerical analysis, 243--269, MAA Stud. Math., 24, Math. Assoc. America, Washington, DC, 1984, MathSciNet.  
36. 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.  
37. Stability analysis of finite difference schemes for the advection-diffusion equation.
    Chan, Tony F.
    SIAM J. Numer. Anal. 21 (1984), no. 2, 272--284, MathSciNet.  
38. Fourth-order finite-difference methods for two-point boundary value problems.
    Bogucz, E. A.; Walker, J. D. A.
    IMA J. Numer. Anal. 4 (1984), no. 1, 69--82, MathSciNet.  
39. 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.  
40. 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.  
41. Finite difference methods for a certain two-point boundary value problem.
    Usmani, Riaz A.
    Indian J. Pure Appl. Math. 14 (1983), no. 3, 398--411, MathSciNet.  
42. Improving the accuracy of finite difference methods for solving boundary value ordinary differential equations.   
    Tewarson, R. P.; Gupta, S.    
    BIT 22 (1982), no. 3, 353--360, MathSciNet.  
43. A finite difference algorithm for coupled nonlinear ordinary differential equations.    
    Dey, S. K.    
    Internat. J. Comput. Math. 10 (1981/82), no. 1, 45--54, MathSciNet.  
44. 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.  
45. 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.  
46. Projection Methods for Two-Point Boundary Value Problems  
    G. W. Reddien  
    SIAM Review, Vol. 22, No. 2. (Apr., 1980), pp. 156-171, Jstor.  
47. 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.  
48. 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.  
49. On consistent finite difference formulae for ordinary differential equations.    
    Miller, R. E.    
    Internat. J. Numer. Methods Engrg. 14 (1979), no. 10, 1567--1573, MathSciNet.  
50. Finite-difference method for generalized eigenvalue problem in ordinary differential equations.
    Antia, H. M.
    J. Comput. Phys. 30 (1979), no. 2, 283--295, MathSciNet.  
51. 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.  
52. 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.  
53. The exact finite-difference solution of a boundary value problem for an ordinary linear second order differential equation. (Russian)     
    Krutoui, B. F.    
    Izv. Tomsk. Politehn. Inst. 277 (1977), 140--147, 205, MathSciNet.  
54. 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.  
55. 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.   
56. 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.  
57. 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.  
58. 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.  
59. 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.  
60. 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.  
61. 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.   
62. 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.  
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. 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.  
65. 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.  
66. Finite difference scheme for a third boundary value problem.
    Zafarullah, A.
    J. Assoc. Comput. Mach. 16 1969 585--591, MathSciNet.  
67. 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.  
68. 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.  
69. Computing eigenvalues of ordinary differential equations by finite differences.    
    Gary, John    
    Math. Comp. 19 1965 365--379, MathSciNet.  
70. An error analysis of finite-difference methods for the numerical solution of ordinary differential equations.    
    Osborne, M. R.    
    Comput. J. 7 1964 232--237, MathSciNet.  
71. A method for finite-difference approximation to ordinary differential equations.    
    Osborne, M. R.    
    Comput. J. 7 1964 58--65, MathSciNet.  
72. A note on finite difference methods for solving the eigenvalue problems of second-order differential equations.
    Osborne, M. R.
    Math. Comp. 16 1962 338--346, MathSciNet.  

(c) John H. Mathews 2003