Runge-Kutta Starters for Multistep Methods

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Runge-Kutta Starters for Multistep Methods

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ACM Transactions on Mathematical Software (TOMS) archive
Volume 6 , Issue 3 (September 1980) table of contents

Pages: 263 - 279

Year of Publication: 1980

ISSN:0098-3500

Author

C. W. Gear

Department of Computer Science, University of Illinois, Urbana, IL

Publisher

ACM New York, NY, USA

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Downloads (6 Weeks): 5, Downloads (12 Months): 49, Citation Count: 4

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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.

	1	~ETTIS, 1).~. Efficient embedded l~unge-l~utta methods In ~vumencat "l"reatment of LP$llerentml Equatmns, vol. 631, R. Burlirsch, R.D. Grigoneff, and J. Schroder, Eds., Lecture Notes in Mathematms, Sprmger-Verlag, New York, 1976.
	2	BUTCHER, J.C. Implicit Runge-Kutta processes Math. Comput. 18 {1964), 50-64.
	3	CAttvzR, M.B. Efficient handhng of discontinuities and time delays in orchnary dlfferenUal equations. In Proc Simulation '77 Symp., Montreux, Switzerland, M. Hamza, Ed., Acta Press, Zurich, Switzerland
	4	E~LE, B.L. A-stable methods and Pade approximations to the exponential. SIAM J. Math. Anal. 4 (1973), 671-680
	5	FEHLBER6, E. Klassiche Runge-Kutta Formeln vierter und medrigerer Ordnung mit Schrittwelten-Kontrolle und im'e Anwendung auf Warmeleltungsprobleme. Computing 6 {1970}, 61-71.
	6	C. W. Gear, Algorithm 407: DIFSUB for solution of ordinary differential equations [D2], Communications of the ACM, v.14 n.3, p.185-190, March 1971 [doi>10.1145/362566.362573]
	7	GEAR, C W. Rational approximations by imphclt Runge-Kutta schemes. BIT 10 (1970), 20-22.
	8	GEAR C.W Runge-Kutta starters for mulhstep methods. Rep. 78-938, Dept. Comput. Scl., Univ. Illinois, Urbana, 1978.
	9	HINDMARSH A.C. GEAR: Ordinary differential equation solver Rep. UCID-30001, Rev. 3, Lawrence Livermore Lab., Llvermore, Cahf., 1974.
	10	HULL, T.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.
	11	KaOGH, F T VODQ/SVDQ/DVDQ--Varlable order integrators for the numerical solution of ordinary differential equations. Sec. 314, Subroutine Write-up, Jet Propulsion Lab., Pasadena, Calif., 1969
	12	NORDSIECK, A. On the numerical mtegraUon of ordinary differential equations. Math. Comput. 16 (1962), 22-49.
	13	SV~AMPINZ, L.F., AND GORDON, M.K. Computer Solutmn of Ordinary Differential Equatmns: The In~tml Value Problem. Freeman, San Francisco, 1975.
	14	STETTER, H.J. Analysts of D~scret~zatmn Methods for Ordinary D~fferent~al Equations, vol 23, Sprmger Tracts in Natural Philosophy, Sprmger-Verlag, New York, 1973.
	15	STETTER, H.J Asymptotm expansions for the error of chscretizatlon algorithms for nonhnear functional equations. Numer. Math. 7 (1965), 18-31

CITED BY 4

	C. W. Gear , O. Osterby, Solving Ordinary Differential Equations with Discontinuities, ACM Transactions on Mathematical Software (TOMS), v.10 n.1, p.23-44, March 1984
	W. H. Enright , K. R. Jackson , S. P. Nørsett , P. G. Thomsen, Interpolants for Runge-Kutta formulas, ACM Transactions on Mathematical Software (TOMS), v.12 n.3, p.193-218, Sept. 1986
	J. R. Cash, Efficient time integrators in the numerical method of lines, Journal of Computational and Applied Mathematics, v.183 n.2, p.259-274, 15 November 2005
	George Corliss , Y. F. Chang, Solving Ordinary Differential Equations Using Taylor Series, ACM Transactions on Mathematical Software (TOMS), v.8 n.2, p.114-144, June 1982