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A note on the effect of conditionally stable correctors


Author: Fred T. Krogh
Journal: Math. Comp. 21 (1967), 717-719
MSC: Primary 65.61
DOI: https://doi.org/10.1090/S0025-5718-1967-0224291-4
MathSciNet review: 0224291
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  • [1] H. J. Stetter, "Stabilizing predictors for weakly unstable correctors," Math. Comp., v. 19, 1965, pp. 84-89. MR 31 #2833. MR 0178576 (31:2833)
  • [2] H. J. Stetter, "A study of strong and weak stability in discretization algorithms," J. Soc. Indust. Appl. Math. Ser. B Numer. Anal., v. 2, 1965, pp. 265-280. MR 32 #4859. MR 0187407 (32:4859)
  • [3] R. L. Crane & R. W. Klopfenstein, "A predictor-corrector algorithm with an increased range of absolute stability," J. Assoc. Comput. Math., v. 12, 1965, pp. 227-241. MR 31 #6378. MR 0182155 (31:6378)
  • [4] F. T. Krogh, "Predictor-corrector methods of high order with improved stability characteristics," J. Assoc. Comput. Mach., v. 13, 1966, pp. 374-385. MR 33 #5127. MR 0196943 (33:5127)
  • [5] B. A. Fuchs & V. I. Levin, Functions of a Complex Variable and Some of Their Applications, Vol. II, Pergamon Press, New York, 1961; Addison-Wesley, Reading, Mass., 1962. MR 24 #A2654. MR 0132818 (24:A2654)
  • [6] E. C. Titchmarsh, The Theory of Functions, Oxford Univ. Press, Oxford, 1939.
  • [7] Anthony 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)
  • [8] F. T. Krogh, "A test for instability in the numerical solution of ordinary differential equations," J. Assoc. Comput. Mach., v. 14, 1967, pp. 351-354. (This gives the stability diagram for the method proposed by Stetter in [1].) MR 0235732 (38:4035)

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DOI: https://doi.org/10.1090/S0025-5718-1967-0224291-4
Article copyright: © Copyright 1967 American Mathematical Society

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