Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 
 

 

Block implicit one-step methods


Authors: L. F. Shampine and H. A. Watts
Journal: Math. Comp. 23 (1969), 731-740
MSC: Primary 65.61
DOI: https://doi.org/10.1090/S0025-5718-1969-0264854-5
MathSciNet review: 0264854
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A class of one-step methods which obtain a block of $ r$ new values at each step are studied. The asymptotic behavior of both implicit and predictor-corrector procedures is examined.


References [Enhancements On Off] (What's this?)

  • [1] D. Morrison & L. Stoller, ``A method for the numerical integration of ordinary differential equations,'' Math. Comp., v. 12, 1958, pp. 269-272. MR 0102180 (21:974)
  • [2] F. Ceschino & J. Kuntzmann, Numerical Solution of Initial Value Problems, Dunod, Paris, 1963; English transl., Prentice-Hall, Englewood Cliffs, N. J., 1966. MR 28 #2639; MR 33 #3465. MR 0195262 (33:3465)
  • [3] J. Butcher, ``Implicit Runge-Kutta processes,'' Math. Comp., v. 18, 1964, pp. 50-64. MR 28 #2641. MR 0159424 (28:2641)
  • [4] J. Rosser, ``A Runge-Kutta for all seasons,'' SIAM Rev., v. 9, 1967, pp. 417-452. MR 36 #2325. MR 0219242 (36:2325)
  • [5] E. Grabbe, S. Ramo & D. Woolridge, Handbook of Automation, Computation and Control. Vol. 1: Control Fundamentals, Chap. 14, pp. 14-60, Wiley, New York, 1958. MR 20 #2093. MR 0095591 (20:2093)
  • [6] V. Krylov, Approximate Calculation of Integrals, Fizmatgiz, Moscow, 1959; English transl., Macmillan, New York, 1962. MR 22 #2002; MR 26 #2008. MR 0144464 (26:2008)
  • [7] L. Rall (Editor), Error in Digital Computation. Vol. I, Wiley, New York, 1965. MR 30 #5510. MR 0175325 (30:5510)
  • [8] G. Dahlquist, ``A special stability problem for linear multistep methods,'' Nordisk Tidskr. Informations-Behandling, v. 3, 1963, pp. 27-43. MR 30 #715. MR 0170477 (30:715)
  • [9] A. Ralston, ``Relative stability in the numerical solution of ordinary differential equations,'' SIAM Rev., v. 7, 1965, pp. 114-125. MR 31 #2831. MR 0178574 (31:2831)
  • [10] P. Henrici, Discrete Variable Methods in Ordinary Differential Equations, Wiley, New York, 1962. MR 24 B1772. MR 0135729 (24:B1772)
  • [11] H. Stetter, ``Stabilizing predictors for weakly unstable correctors,'' Math. Comp., v. 19, 1965, pp. 84-89. MR 31 #2833. MR 0178576 (31:2833)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65.61

Retrieve articles in all journals with MSC: 65.61


Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1969-0264854-5
Article copyright: © Copyright 1969 American Mathematical Society

American Mathematical Society