The use of exponential sums in step by step integration

Authors:
P. Brock and F. J. Murray

Journal:
Math. Comp. **6** (1952), 63-78

MSC:
Primary 65.0X

DOI:
https://doi.org/10.1090/S0025-5718-1952-0047403-3

MathSciNet review:
0047403

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References | Similar Articles | Additional Information

**[1]**W. E. Milne,*The remainder in linear methods of approximation*, J. Research Nat. Bur. Standards**43**(1949), 501–511. MR**0036279****[2]**Robert E. Greenwood,*Numerical integration for linear sums of exponential functions*, Ann. Math. Statistics**20**(1949), 608–611. MR**0032216****[3]**P. Brock & F. J. Murray, ``Planning and error analysis for the numerical solution of a test system of differential equations on the IBM sequence calculator,''*Cyclone Report*, Reeves Instrument Corp., New York 28. See also F. J. Murray, ``Planning and error considerations for the numerical solution of a system of differential equations on a sequence calculator,''*MTAC*, v. 4, p. 133-144.**[4]**F. J. Murray,*Linear equation solvers*, Quart. Appl. Math.**7**(1949), 263–274. MR**0031329**, https://doi.org/10.1090/S0033-569X-1949-31329-0**[5]**L. H. Thomas of the Watson Scientific Computing Laboratory indicated this formula for to the authors. He also indicated that the are equal in absolute value to the coefficients of the Adams-Bashforth method of step by step numerical integration.**[6]**W. Feller,*Probability Theory*. New York, 1950, v. 1, p. 52.**[7]**G. Birkhoff & S. MacLane,*A Survey of Modern Algebra*. New York, 1948, p. 424.

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DOI:
https://doi.org/10.1090/S0025-5718-1952-0047403-3

Article copyright:
© Copyright 1952
American Mathematical Society