Recurrence relations for computing with modified divided differences

Krogh, Fred T.

doi:10.1090/S0025-5718-1979-0537970-4

Recurrence relations for computing with modified divided differences
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Math. Comp. 33 (1979), 1265-1271 Request permission

Corrigendum: Math. Comp. 35 (1980), 1445.
Corrigendum: Math. Comp. 35 (1980), 1445.

Abstract:

Modified divided differences (MDD) provide a good way of representing a polynomial passing through points with unequally spaced abscissas. This note gives recurrence relations for computing coefficients in either the monomial or Chebyshev basis from the MDD coefficients, and for computing the MDD coefficients for either the differentiated or the integrated polynomial. The latter operation is likely to be useful if MDD are used in a method for solving stiff differential equations.

References

Gertrude Blanch, On modified divided differences. II, Math. Tables Aids Comput. 8 (1954), 67–75. MR 61883, DOI 10.1090/S0025-5718-1954-0061883-0
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
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
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

The Computation of Coefficients of Variable-Step Adams Methods

F. B. Hildebrand, Introduction to numerical analysis, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1956. MR 0075670
Herbert E. Salzer, A recurrence scheme for converting from one orthogonal expansion into another, Comm. ACM 16 (1973), no. 11, 705–707. MR 0395158, DOI 10.1145/355611.362548