Limiting precision in differential equation solvers

Limiting precision in differential equation solvers
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by L. F. Shampine PDF

Math. Comp. 28 (1974), 141-144 Request permission

Machine dependent limits on the step size and local error tolerance are discussed. By taking them into account codes can be made more robust.

References

L. F. Shampine and M. K. Gordon, Computer solution of ordinary differential equations, W. H. Freeman and Co., San Francisco, Calif., 1975. The initial value problem. MR 0478627
Fred T. Krogh, A variable step, variable order multistep method for the numerical solution of ordinary differential equations, Information Processing 68 (Proc. IFIP Congress, Edinburgh, 1968) North-Holland, Amsterdam, 1969, pp. 194–199. MR 0261790
Lawrence F. Shampine and Richard C. Allen Jr., Numerical computing: an introduction, W. B. Saunders Co., Philadelphia-London-Toronto, Ont., 1973. MR 0359250
C. William Gear, Numerical initial value problems in ordinary differential equations, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1971. MR 0315898

JACM

Fred T. Krogh, Changing stepsize in the integration of differential equations using modified divided differences, Proceedings of the Conference on the Numerical Solution of Ordinary Differential Equations (Univ. Texas, Austin, Tex., 1972) Lecture Notes in Math., Vol. 362, Springer, Berlin, 1974, pp. 22–71. MR 0362908
Emil Vitásek, The numerical stability in solution of differential equations, Conf. on Numerical Solution of Differential Equations (Dundee, 1969) Springer, Berlin, 1969, pp. 87–111 (2 graphs). MR 0267779
E. K. Blum, A modification of the Runge-Kutta fourth-order method, Math. Comp. 16 (1962), 176–187. MR 145661, DOI 10.1090/S0025-5718-1962-0145661-4