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