| Global Error Estimates for Ordinary Differential Equations |
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ACM Transactions on Mathematical Software (TOMS)
archive
Volume 2 , Issue 2 (June 1976)
table of contents
Pages: 172 - 186
Year of Publication: 1976
ISSN:0098-3500
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Authors
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L. F. Shampine
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Division 2642, Sandia Laboratories, Albuquerque, NM
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H. A. Watts
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Division 2642, Sandia Laboratories, Albuquerque, NM
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| Bibliometrics |
Downloads (6 Weeks): 10, Downloads (12 Months): 55, Citation Count: 8
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REFERENCES
Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.
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BLUM, E.K. A modification of the Runge-Kutta fourth order method. Math. Computation 16 (1962), 176-187.
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BUTCHER, J.C. The effective order of Runge-Kutta methods. Conf. on the Numerical Solutions of Differential Equations, Lecture Notes m Mathematms No. 109, Springer Verlag, 1969, pp. 133-139.
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FE~LBERG, E. Low-order classical Runge-Kutta formulas w~th step-size control and their apphcation to some heat transfer problems. NASA Tech. Rep. TR R-315, George C. Marshall Space Flight Center, Marshall, Ala.
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HENRICI, P. D~screte Variable Methods for Ordinary D~fferential Equations. Wiley, New York, 1962.
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HULL, T.E., ENRmHT, W.H., FELLEN, B.M., h~D SEDGWlCK, A.E. Comparing numerical methods for ordinary differential equations. SIAM J. Numer. Anal. 9 (1972), 603-637.
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LETHER, F.G. The use of Richardson extrapolation in one-step methods with variable step-size. Math. Computation 20 (1966), 379-385.
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SHAMPINE, L.F. Limiting precision in differential equation solvers. Math. Computation ~8 (1974), 141-144.
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SHAMPINE, L.F. Local extrapolation in the solution of ordinary differential equations. Math. Computation 27 (1973), 91-97.
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SHAMPINE, L.F., AN}) GORDON, M.K. Computer Solution of Ordinary Differential Equations: The Initial Value Problem. Freeman, San Francisco, Calif., 1975.
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SHAMPIN~, L.F., AND WATTS, H.A. Comparing error estimators for Runge-Kutta methods. Math. Computation ~5 (1971), 445-455.
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SHAMPINE, L.F., WATTS, tt.A., AND DAVESPORT, S.M. Solving non-stiff ordinary differential equations--the state of the art. To appear in SIAM Rev.
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STETTER, H.J. Local estimation of the global discretization error. SIAM J. Numer. Anal. 8 (1971), 512-523.
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VITASEK, E. The numerical stability in solution of differential equations. Conf. on the Numerical Solution of Differential Equations, Lecture Notes in Mathematics No. 109, Springer Verlag, 1969, pp. 87-111.
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