Local extrapolation in the solution of ordinary differential equations

Mathematics of Computation

Volumn 27, Issue 121, 1973, Pages 91-97

  Shampine, L F ^a  

^a SANDIA NATIONAL LABORATORIES   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84968517891     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-1973-0331803-1     Document Type: Article

References (10)

1. L. F. Shampine & H. A. Watts, “Comparing error estimators for Runge-Kutta methods,” Math. Comp., v. 25, 1971, pp. 445-455.
2. J. A. Zonneveld, Automatic Numerical Integration, Math. Centre Tracts, no. 8, Mathematisch Centrum, Amsterdam, 1964. MR 30, #1612.
3. C. W. Gear, Numerical Initial Value Problems in Ordinary Differential Equations, Prentice-Hall, Englewood Cliffs, N. J., 1971.
4. E. Fehlberg, “Klassische Runge-Kutta-Formeln vierter und niedrigerer Ordnung mit Schrittweiten-Kontrolle und ihre Anwendung auf Wärmeleitungsprobleme,” Computing (Arch. Elektron. Rechnen), v. 6, 1970, pp. 61-71. MR 43 #5728.
5. H. Shintani, “Two-step processes by one-step methods of order 3 and of order 4,” J. Sei. Hiroshima Univ. Ser. A-l Math., v. 30, 1966, pp. 183-195. MR 34 #7032.
6. P. Henrici, Discrete Variable Methods in Ordinary Differential Equations, Wiley, New York, 1962. MR 24 #B1772.
7. F. T. Krogh, VODQ/SVDQ/DVDQ-Faria6/e Order Integrators for the Numerical Solution of Ordinary Differential Equations, TU Doc. No. CP-2308, NPO-11643, May 1969; On Testing A Subroutine for the Numerical Integration of Ordinary Differential Equations, JPL Internal Document, Section 314, TM No. 217 (revised), October 1970, Jet Propulsion Laboratory, Pasadena, Calif.
8. R. W. Hamming, “Stable predictor-corrector methods for ordinary differential equations,” J. Assoc. Comput. Math., v. 6, 1959, pp. 37-47. MR 21 #973.
9. R. W. Hamming, Numerical Methods for Scientists and Engineers, Internat. Series in Pure and Appl. Math., McGraw-Hill, New York, 1962. MR 25 #735.
10. L. F. Shampine, Stability Regions for Extrapolated Runge-Kutta and Adams Methods, SC-RR-72 0223, March 1972.