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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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KROGH, :FRED T. VODQ/SVDQ/DVDQ--Variable order integrators for the numerical solution of ordinary differential equations. Section 314 subroutine write-up, Jet Propulsion Laboratory, Pasadena, Calif., May 1969.
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2
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KROGH, FRED W. A variable step variable order multistep method for the numerical solution of ordinary differential equations. Information Processing 68, Proc. IFIP Congress 1968, North- Holland, Amsterdam, 1969, pp. 194-199.
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FEHLBERG, ERW~N. New one-step integration methods of high-order accuracy applied to some problems in celestial mechanics. NASA TR R-248, NASA Tech. Rep., Oct. 1966.
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4
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BULIRSCH, ROLAND, AND STOER, JOSEF. Numerical treatment of ordinary differential equations by extrapolation methods. Numer. Math. 8 (1966), 1-13.
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CLARK, NANCY W. A study of some numerical methods for the integration of systems of firstorder ordinary differential equations. Rep. % ANL-7428, Argonne National Laboratory, Argonne, Ill., March 1968.
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8
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RATLIFF, K. A Comparison of Techniques for the Numerical Integration of Ordinary Differential Equations. Rep. ~274, Dep. of Computer Science, University of Illinois, Urbana, Ill., July 1968.
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9
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GEAR, C.W. The automatic integration of stiff ordinary differential equations, information Processing 68, Proc. IFIP Congress 1968, North-Holland, Amsterdam, 1969, pp. 187-193.
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10
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BROOKS, JOHN D., AND POPE, DAVID A. Asymptotic error estimates and the numerical solution of the equations of orbital motion. SIAM J. Numer. Anal. ~ (1967), 446-456.
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11
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DEVINE, C. J. Accuracy studies of a second-sum Adams-type predictor-corrector numerical integrator. JPL Space Programs Summary No. 37-22, Vol. IV, 1965, pp. 3-10.
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12
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DEVINE, C.J. Numerical integration over a family of ellipses using a second-sum multi-step integrator employing high-order backward differences, jPL Space Programs Summary No. 37-33, Vol. IV, 1965, pp. 11-15.
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GALLAHER, LAWRENCE J., AND PERLIN, IRWIN E. A comparison of several methods of numerical integration of nonlinear differential equations. Rich Electronic Computer Center, Georgia institute of Technology, Atlanta, Georgia (presented at the SIAM National Meeting, March 1966).
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14
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KELLER, H. B. Numerical Methods for Two-Point Boundary Value Problems. Blaisdell, Waltham, Mass., 1968.
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OSBORNE, M.R. On shooting methods for boundary value problems. J. Math. Analysis and Applications 27 (1969), 417-433.
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CaANE, P. C., AND Fox, P. A. A comparative study of computer programs for integrating differential equations. Bell Telephone Laboratories Numerical Mathematics Computer Programs, Library One-Basic Routines for General Use, Vol. 2, Issue 2, 1969.
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HANSON, RICHARD J., AND LAWSON, CHARLI';S L. Extensions and applications of the Householder algorithm for solving linear least squares problems. Math. Comput. 25 (1969), 787-812.
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HULL, W. E., ENRIGHT, W. H., FELLEN, B. M., AND SEDGWICK, A. E. Comparing numerical methods for ordinary differential equations. SIAM J. Numer. Anal. 9 (1972), 603-637. (This paper includes our program {1} in comparisons which are made.)
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KROG~, FRED T. Algorithms for changing the stepsize used by a multistep method. SIAM J. Numer. Anal. 10 (1973) (to appear). (Gives method used by {1} for changing the stepsize.)
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KROGH, FRED T. Changing stepsize in the integration of differential equations using modified divided differences. To appear in the proceedings of the SIAM/AAS conference " Numerical Solution of Ordinary Differential Equations," to be published by Springer-~erlag in their series "Lecture Notes in Mathematics." (Gives some of the details of the order selection and the stepsize selection processes used in {1}.)
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