Recurrence relations for computing with modified divided differences

Author:
Fred T. Krogh

Journal:
Math. Comp. **33** (1979), 1265-1271

MSC:
Primary 65L99; Secondary 65D99

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

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

MathSciNet review:
537970

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Abstract | References | Similar Articles | Additional Information

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.

**[1]**G. BLANCH, "On modified divided differences,"*Math. Comp.*, v. 8, 1954, pp. 1-11, 67-75. MR**0061883 (15:900d)****[2]**F. T. KROGH, "A variable step variable order multistep method for the numerical solution of ordinary differential equations,"*Information Processing*68 (Proceedings of the IFIP Congress, 1968), North-Holland, Amsterdam, 1961, pp. 194-199. MR**0261790 (41:6402)****[3]**F. 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*, October 1972, Lecture Notes in Math., vol. 362, Springer-Verlag, New York, 1974, pp. 22-71. MR**0362908 (50:15346)****[4]**L. F. SHAMPINE & M. K. GORDON,*Computer Solution of Ordinary Differential Equations, The Initial Value Problem*, Freeman, San Francisco, Calif., 1975. MR**0478627 (57:18104)****[5]**L. W. JACKSON,*The Computation of Coefficients of Variable-Step Adams Methods*, Technical Report No. 94, Dept. of Comput. Sci., Univ. of Toronto, 1976.**[6]**F. B. HILDEBRAND,*Introduction to Numerical Analysis*, McGraw-Hill, New York, 1956. MR**0075670 (17:788d)****[7]**H. E. SALZER, "A recurrence scheme for converting from one orthogonal expansion into another,"*Comm. ACM*, v. 16, 1973, pp. 705-707. MR**0395158 (52:15956)**

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DOI:
http://dx.doi.org/10.1090/S0025-5718-1979-0537970-4

Article copyright:
© Copyright 1979
American Mathematical Society