Bibliography for the

Adams Bashforth Moulton Method for O.D.E.'s

Return to Numerical Methods - Numerical Analysis

 

  1. Improvement of the Stability of the Estuarine Coastal Ocean Model by A Predictor -Corrector Scheme
    Zhu, J.-R.; Yang, L.-H.; Zhu, S.-X.
    Oceanologia et Limnologia Sinica, 2002, vol. 33, no. 1, pp. 15-22, Ingenta.  
  2. A first-order sequential predictor-corrector regularization method for ill-posed Volterra equations.    
    Ring, Wolfgang    
    SIAM J. Numer. Anal. 38 (2001), no. 6, 2079--2102 (electronic), MathSciNet.   
  3. Accuracy of multivalue methods during change of time-step size: Adams-Moulton.    
    Gray, William G.; Muccino, Julia C.    
    Numer. Methods Partial Differential Equations 16 (2000), no. 3, 312--326, MathSciNet.  
  4. Modified Adams-Moulton predictor-corrector method in solving multibody dynamical systems.   
    Wu, S. D.; Chiou, J. C.; Lin, Y. C.
    Mech. Structures Mach. 28 (2000), no. 2-3, 201--218, MathSciNet.   
  5. Alternative stepsize strategies for Adams predictor-corrector codes.   
    Usman, Anila; Hall, George   
    J. Comput. Appl. Math. 116 (2000), no. 1, 105--120, MathSciNet.   
  6. An explicit predictor-corrector solver with application to seismic wave modelling.
    Phadke, Suhas; Bhardwaj, Dheeraj; Dey, S.K.
    Computers & geosciences, 2000, vol. 26, no. 9/10, pp. 1053, Ingenta.  
  7. On the generation of higher order numerical integration methods using lower order Adams-Bashforth and Adams-Moulton methods.    
    Chiou, J. C.; Wu, S. D.    
    J. Comput. Appl. Math. 108 (1999), no. 1-2, 19--29, MathSciNet.  
  8. A Predictor-Corrector Scheme for Open Boundary Problems.
    Aiello, G.; Alfonzetti, S.; Salerno, N.
    IEEE transactions on magnetics, 1998, vol. 34, no. 5p1, pp. 2573, Ingenta.  
  9. Remarks on extended Milne's device for the Adams PC methods.    
    Fujii, Masatomo; Hayashi, Yuichi    
    Bull. Fukuoka Univ. Ed. III 46 (1997), 23--30.
  10. Approximation of Ill-Posed Volterra Problems via Predictor-Corrector Regularization Methods  
    Patricia K. Lamm
    SIAM Journal on Applied Mathematics, Vol. 56, No. 2. (Apr., 1996), pp. 524-541, Jstor.  
  11. An explicit high order predictor-corrector method for periodic initial value problems.   
    Simos, T. E.   
    Math. Models Methods Appl. Sci. 5 (1995), no. 2, 159--166, MathSciNet.   
  12. A family of four-step exponentially fitted predictor-corrector methods for the mumerical integration of the schrodinger equation.
    Simos, T.E.
    Journal of computational and applied mathematics, 1995, vol. 58, no. 3, pp. 337, Ingenta.  
  13. Predictor-Corrector Phase-Fitted Methods for Y" = F(X,Y) and an Application to the Schrodinger Equation.
    Simos, T.E.
    International journal of quantum chemistry. Qua, 1995, vol. 53, no. 5, pp. 473, Ingenta.  
  14. Hermite predictor-corrector scheme for regular Volterra integral equations and for some integro-differential equations of turbulent diffusion.   
    Khanh, Bui Doan   
    J. Comput. Appl. Math. 51 (1994), no. 3, 305--316, MathSciNet.   
  15. A Self-Checking Predictor-Corrector Algorithm for Efficient Evaluation of Reflector Antenna Radiation Integrals.
    Moreira, F.J.S.; Prata, A.
    IEEE transactions on antennas and propagation, 1994, vol. 42, no. 2, pp. 246, Ingenta.  
  16. A predictor-corrector phase fitted method for y"=f(x,y).
    Simos, T.E.
    Mathematics and computers in simulation, 1993, vol. 35, no. 2, pp. 153, Ingenta.  
  17. Predictor-Corrector Guidance Algorithm for Use in High-Energy Aerobraking System Studies.
    Braun, R.D.; Powell, R.W.
    Journal of guidance, control, and dynamics, 1992, vol. 15, no. 3, pp. 672, Ingenta.  
  18. An extension of Milne's device for the Adams predictor-corrector methods.   
    Fujii, Masatomo   
    Japan J. Indust. Appl. Math. 8 (1991), no. 1, 1--18, MathSciNet.   
  19. Variable order Adams-Bashforth predictors with an error-stepsize control for continuation methods.   
    Lundberg, Bruce N.; Poore, Aubrey B.    
    SIAM J. Sci. Statist. Comput. 12 (1991), no. 3, 695--723, MathSciNet.  
  20. A new family of real-time predictor-corrector integration algorithms.
    Howe, R.M.
    Simulation, 1991, vol. 57, no. 3, pp. 177, Ingenta.  
  21. New Predictor Corrector Trapezoidal Formulae for Solving Initial Value Problems.
    Sanugi, B.B.; Evans, D.J.
    International journal of computer mathematics, 1990, vol. 33, no. 1/2, pp. 77, Ingenta.  
  22. A sixth order predictor-corrector method for periodic IVPs.   
    Voss, D. A.; Khaliq, A. Q. M.   
    Appl. Math. Lett. 2 (1989), no. 1, 65--68, MathSciNet.   
  23. New Predictor Corrector Formulas for Initial Value Problems in ordinary Differential Equations.
    Fatunla, Simeon Ola
    International journal of computer mathematics, 1989, vol. 26, no. 3/4, pp. 247, Ingenta.  
  24. Extended Adams-Moulton methods.    
    Xu, Xu Hai    
    J. Math. (Wuhan) 8 (1988), no. 4, 339--344, MathSciNet.  
  25. Quasilinear Multistep Methods and Variable Step Predictor-Corrector Methods for Neutral Functional Differential Equations  
    Zdzislaw Jackiewicz  
    SIAM Journal on Numerical Analysis, Vol. 23, No. 2. (Apr., 1986), pp. 423-452, Jstor.   
  26. Variable Step Size Predictor-Corrector Schemes for Second Kind Volterra Integral Equations  
    H. M. Jones, S. McKee  
    Mathematics of Computation, Vol. 44, No. 170. (Apr., 1985), pp. 391-404, Jstor.   
  27. Turbulence in Multistep Methods for Initial Value Problems  
    Michael Prufer  
    SIAM Journal on Applied Mathematics, Vol. 45, No. 1. (Feb., 1985), pp. 32-69, Jstor.  
  28. One-Step Collocation: Uniform Superconvergence, Predictor-Corrector Method, Local Error Estimate  
    Marino Zennaro  
    SIAM Journal on Numerical Analysis, Vol. 22, No. 6. (Dec., 1985), pp. 1135-1152, Jstor.   
  29. The Convergence of Variable-Stepsize, Variable-Formula, Multistep Methods  
    M. Crouzeix, F. J. Lisbona  
    SIAM Journal on Numerical Analysis, Vol. 21, No. 3. (Jun., 1984), pp. 512-534, Jstor.   
  30. Adams-Barthforth [Bashforth] formula.    
    Bhaskara Murthy, V. S.    
    Math. Ed. (Siwan) 18 (1984), no. 2, 77--80, MathSciNet.  
  31. Interpolation and error estimation in Adams PC-codes.    
    Stetter, Hans J.    
    SIAM J. Numer. Anal. 16 (1979), no. 2, 311--323.
  32. The Application of Linear Multistep Methods to Singular Initial Value Problems  
    Frank R. de Hoog, Richard Weiss  
    Mathematics of Computation, Vol. 31, No. 139. (Jul., 1977), pp. 676-690, Jstor.  
  33. On Comparing Adams and Natural Spline Multistep Formulas  
    David R. Hill  
    Mathematics of Computation, Vol. 29, No. 131. (Jul., 1975), pp. 741-745, Jstor.  
  34. Some New Multistep Methods for Solving Ordinary Differential Equations  
    G. K. Gupta, C. S. Wallace  
    Mathematics of Computation, Vol. 29, No. 130. (Apr., 1975), pp. 489-500, Jstor.  
  35. Stability Analysis of Predictor-Corrector Algorithms of Adams Type  
    George Hall  
    SIAM Journal on Numerical Analysis, Vol. 11, No. 3. (Jun., 1974), pp. 494-505, Jstor.   
  36. Exponential Fitting of Matricial Multistep Methods for Ordinary Differential Equations  
    E. F. Sarkany, W. Liniger  
    Mathematics of Computation, Vol. 28, No. 128. (Oct., 1974), pp. 1035-1052, Jstor.  
  37. Stability and Convergence of Variable Order Multistep Methods  
    C. W. Gear, D. S. Watanabe  
    SIAM Journal on Numerical Analysis, Vol. 11, No. 5. (Oct., 1974), pp. 1044-1058, Jstor.  
  38. The Effect of Variable Mesh Size on the Stability of Multistep Methods  
    C. W. Gear, K. W. Tu  
    SIAM Journal on Numerical Analysis, Vol. 11, No. 5. (Oct., 1974), pp. 1025-1043, Jstor.  
  39. A Predictor-Corrector Method for a Certain Class of Stiff Differential Equations  
    Karl G. Guderley, Chen-Chi Hsu  
    Mathematics of Computation, Vol. 26, No. 117. (Jan., 1972), pp. 51-69, Jstor.   
  40. Predictor-Corrector Algorithms with Identical Regions of Stability  
    J. D. Lambert  
    SIAM Journal on Numerical Analysis, Vol. 8, No. 2. (Jun., 1971), pp. 337-344, Jstor.   
  41. Cyclic Composite Multistep Predictor-Corrector Methods  
    John Donelson III, Eldon Hansen  
    SIAM Journal on Numerical Analysis, Vol. 8, No. 1. (Mar., 1971), pp. 137-157, Jstor.   
  42. A Note on the Stability of Predictor-Corrector Techniques  
    James Case  
    Mathematics of Computation, Vol. 23, No. 108. (Oct., 1969), pp. 741-749, Jstor.   
  43. Numerical Stability of a One-Evaluation Predictor-Corrector Algorithm for Numerical Solution of Ordinary Differential Equations  
    R. W. Klopfenstein, R. S. Millman  
    Mathematics of Computation, Vol. 22, No. 103. (Jul., 1968), pp. 557-564, Jstor.   
  44. An Analysis of the Numerical Stability of Predictor-Corrector Solutions of Nonlinear Ordinary Differential Equations  
    Robert J. Lambert  
    SIAM Journal on Numerical Analysis, Vol. 4, No. 4. (Dec., 1967), pp. 597-606, Jstor.   
  45. A Predictor-Corrector Type Scheme for the Mixed Boundary Problem for a Hyperbolic First-Order System in Two Dimensions  
    Vidar Thomee  
    Journal of the Society for Industrial and Applied Mathematics, Vol. 11, No. 4. (Dec., 1963), pp. 964-975, Jstor.   
  46. On Predictor-Corrector Methods for Nonlinear Parabolic Differential Equations  
    Jim Douglas, Jr., B. F. Jones, Jr.  
    Journal of the Society for Industrial and Applied Mathematics, Vol. 11, No. 1. (Mar., 1963), pp. 195-204, Jstor.   
  47. Corrector Formulas for Multi-Step Integration Methods  
    T. E. Hull, A. C. R. Newbery  
    Journal of the Society for Industrial and Applied Mathematics, Vol. 10, No. 2. (Jun., 1962), pp. 351-369, Jstor.  
  48. An extension of Milne's three-point method.   
    Keitel, Glenn H.   
    J. Assoc. Comput. Mach. 3 (1956), 212--222.

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2003