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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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BJUREL, G., DAHLQUIST, G., LINDBERG, B., LINDE, S., AND ODEN, L.. Survey of stiff ordinary differential equations. Rep. NA 70.11, Dep. of Information Processing, Royal Inst. Technology, S-100 44, Stockholm, Nov. 1972.
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BRAYTON, R. K., GUSTAVSON, F. G., AND HACHT:EL, G. D. 2~k new efficient algorithm for solving differential-algebraic systems using implicit backward differentiation formulas. Proc. IEEE 60 (1972), 98-108.
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CAVENDISH, J. C., CULHAM, W. E., AND VARQA, R. S. A comparison of Crank-Nicolson and Chebyshev-rational methods for numerically solving linear parabolic equations. J. Computational Phys. 10 (1972), 354-368.
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CHANG, J. S., HINDMARSH, A. C., AND MADSEN, N.K. Simulation of chemical kinetics transport in the stratosphere. Rep. UCRL-74823, Lawrence Livermore Lab., U. of California, Livermore, Calif., Oct. 1973. (Also in St~fl D~fferent~al Systems, R. A. Wffioughby, Ed., Plenum Press, New York, 1974, pp. 51-65.)
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CODDINGTON, E. A., AND LEVINSON, N. Theory of Ordinary Differential Equations. McGraw- Hill, New York, 1955.
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CODY, W. J., MEINARDUS, G., AND VARGA, R. S. Chebyshev rational approximations to e-~ in {0, -{- ~~) and applications to heat conduction problems. J. Approximation Theory (1969), 50-65.
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CnANS, P. C., AND FOX, P. A. A comparative study of computer programs for integrating differential equations. In Numerical Mathematics Computer Programs, Library One--Basic Routines for General Use, Vol. 2, Issue 2, Numerical Mathematics Program Library Project, Computer Sci. Res. Cent., Bell Telephone Lab., Inc., Murray Hill, N.J., Feb. 1969.
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CURTISS, C. F., AND HmSCHFELDER, J. O. Integration of stiff equations. Proc. Nat. Acad~ Sci. U.S.A. 38 (1952), 235-243.
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DICKINSON, R. P., JR. Private communication.
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EHL~, B. L. A comparison of some methods for solving certain stiff ordinary differential equations. Rep. 70, Dep. of Math., U. of Victoria, Victoria, B.C., Canada, Nov. 1972.
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GEAR, C.W. Asymptotic estimation of errors and derivatives for the numerical solution of ordinary differential equations. UIUCDCS-R-73-598, U. of Illinois, Urbana, Ill., Oct. 1973; also, in Information Processing 74 (IFIP 74), Vol. 3, North-Holland, Amsterdam, 1974, pp. 447--451.
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GEAa, C. W., AND TU, K.-W. The effect of variable mesh size on the stability of multistep methods. UIUCDCS-R-73-570, U. of Illinois, Urbana, Ill., April 1973. (Also in SIAM J. Numer. Anal. 11 (1974), 1025--1043.)
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GEAR, C. W., AND WATANABE, D.S. Stability and convergence of variable order multistep methods. SIAM J. Numer. Anal. 11 (1974), 1044-1058.
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GELINAS, R. J. Diurnal kinetic modelling. UCRL-75373, Lawrence Livermore Lab., U. of California, Livermore, Calif., Jan. 1974. (To appear in Proc. of the IAMAP/IAPSO Conf., Melbourne, Australia, Jan. 14-25, 1974 )
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HALE, J.K. Ordinary Dlfferentml Equations. Wiley-Interscience, New York, 1969.
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Hv.sR:ci, P. Discrete Variable Methods in Ordinary Differential Equatwns. Wiley, New York, 1962.
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HINDMARSH, A. C. GEAR: ordinary differential equation system solver. UCID-30001, Rev. 2, Lawrence Livermore Lab., U. of California, Livermore, Calif., Aug. 1972.
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HINDMARSH, A. C. The construction of mathematical software, part III: the control of error in the GEAR package for ordinary differential equations. UCID-30050, Pt. 3, Lawrence Livermore Lab, U. of Cahfornia, Livermore, Calif., Aug. 1972.
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HINDMAaSH, A. C. Linear multistep methods for ordinary differential equations: method formulations, stability, and the methods of Nordsieck and Gear. UCRL-51186, Rev. 1, Lawrence Livermore Lab., U. of California, Livermore, Calif., March 1972.
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HIm)MARSH, A. C. GEARB: solution of ordinary differential equations having banded Jacobian. UCID-30059, Lawrence Livermore Lab., U. of California, Livermore, Calif., May 1973.
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HULL, T. E., ENRIGHT, W. H., FELLEN~ B. M., AND SEDGWICK, A. :E. Comparing numerical methods for ordinary differential equations. SIAM J. Namer. Anal. 9 (1972), 603-637.
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KROGH, F.T. A variable step variable order multistep method for the numerical solution of ordinary differential equations. In Information Processing 68 (Proc. IFIP 68), Vol. I, A. J. H. Morrell, Ed., North-Holland, Amsterdam, 1969, pp. 194-199.
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KaoGE, F.T. Changing stepsize in the integration of differential equations using modified divided differences. Proc. of the Conf. on the Numerical Solutmn of Ordinary Dlfferentml Equatmns, U. of Texas at Austin, Oct. 19--20, 1972, D. G. Bett~s, Ed., Lecture Notes in Mathematics, Vol. 362, Springer-Verlag, New York, 1974, pp. 22-71.
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LAPIDUS, L., AND S:EINFELD, j. H. Numerical Solution of Ordinary Dzfferential Equations. Academic Press, New York, 1971.
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LINIGER, W., AND WILLOUGHBY, R. Efficient integration methods for stiff systems of ordinary differential equations. SIAM J. Numer. Anal. 7 (1970), 47-66.
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MADSEN, N. K, AND SINCOVEC, R. F. The numerical method of lines for the solution of nonhnear partmi differential equations. UCRL-75142, Lawrence Livermore Lab., U. of Califorma, Livermore, Calif., Sept. 1973.
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M)~KELA, M. On a generalized interpolation approach to the numerical integration of ordinary dlfferentml equations. A z~,. Acad. Sc~. Fenn~cae, Ser. A, I, 503 (1973), 1-43.
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MILNE, W.E. A note on the numerical integration of differential equations. J. Res. Nat. Bur. Stand. ~3 (1949), 537-542.
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MILNE, W.E. Numerical Solution of D~fferential Equatwns, Wiley, New York, 1953.
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M~LNE-THOMSON, L.M. The Calculus of Finite D,fferences. Macmillan, London, 1933.
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NORDSIECK, A. On the numerical integration of ordinary differential equations. Math.{ Computation 16 (1962), 22-49.
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ODEH, F., AND LINIGER, W. A note on the unconditional fixed-h stability of linear multistep formulae Computing 7 (1971), 240-253.
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PIOTROWSKY, P. Stability, consistency and convergence of variable K-step methods. In Conf. on the Nun~erical Solution of Differential Equations, J. L. Morris, Ed., Lecture Notes in Mathematics, Vol. 109, Sprmger-Verlag, New York, 1969, pp. 221-227.
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RICE, J. R. On the construction of polyalgorithms for automatic numerical analysis. In Interactwe Systems for Experimental Applied Mathematzcs, M. Klerer and J. Reinfelds, Eds., Academic Press, New York, 1968, pp. 301-313.
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RUBN~.R-PETERSON, T. An efficient algorithm using backward time-scaled differences for solving stiff differential-algebraic systems. Tech. U. of Denmark, 2800 Lyngby. Sept. 1973. Presented at the Seminar in Numerical Analysis, Royal Inst. of Technology, Stockholm, Oct. 10-12, 1973.
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SCHECTER, R.S. The Variatzonal Method in Engineering. McGraw-Hill, New York, 1967.{
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SHAMPINE, L. F., AND GORDON, M.K. Computer Solution of Ordinary D~fferential Equations: Initial Value Problems. In press, Freeman, San Francisco, Calif.
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SHAMPINE, L. F., AND GORDON, M.K. Local error and variable order Adams codes. A ppl. Math. Computation, to appear.
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45
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SINCOVEC, R.F. Private communication.
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STETTER, I-I. J. Asymptotic expansions for the error of discretization algorithms for nonlinear{ functional equations. Numer. Math. 7 (1965), 18-31.
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Tu, K.-W. Stability and convergence of general multistep and multivalue methods with variable step size. UIUCDCS-R-72-526, U. of Illinois, Urbana, Ill., July 1972. (Also Ph.D. Th., Dep. of Math., U. of Ilhnois, 1972.)
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CITED BY 16
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Alan C. Hindmarsh , Peter N. Brown , Keith E. Grant , Steven L. Lee , Radu Serban , Dan E. Shumaker , Carol S. Woodward, SUNDIALS: Suite of nonlinear and differential/algebraic equation solvers, ACM Transactions on Mathematical Software (TOMS), v.31 n.3, p.363-396, September 2005
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