An Implementation of a Class of Stabilized Explicit Methods for the Time Integration of Parabolic Equations

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An Implementation of a Class of Stabilized Explicit Methods for the Time Integration of Parabolic Equations

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ACM Transactions on Mathematical Software (TOMS) archive
Volume 6 , Issue 2 (June 1980) table of contents

Pages: 188 - 205

Year of Publication: 1980

ISSN:0098-3500

Author

J. G. Verwer

Mathematisch Centrum, 2e Boerhaavestraat 49, 1091 AL Amsterdam, The Netherlands

Publisher

ACM New York, NY, USA

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Downloads (6 Weeks): 1, Downloads (12 Months): 24, Citation Count: 2

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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	BAKKER, M Software for seml-dlscretlzatlon of time dependent partial differential equations in one space variable Rep. NW 52/77, Mathematlsch Centrum, Amsterdam, 1977.
	2	BAKKER, M. Unpubhshed manuscmpt. Mathematisch Centrum, Amsterdam.
	3	BEENTJES, P.A. NUMAL, A hbrary of ALGOL 60 procedures m numerical mathematics. Mathematlsch Centrum, Amsterdam, 1974, sec 5.2.1.1 1.1., procedure ARK.
	4	DOUGLAS, J., AND DUPONT, T Galerkin methods for parabolic equations. SIAM j. Numer. Anal 7 (1970), 575-626.
	5	C. William Gear, Numerical Initial Value Problems in Ordinary Differential Equations, Prentice Hall PTR, Upper Saddle River, NJ, 1971
	6	LINDBERG, B IMPEX--A program package for solution of systems of stiff differential equations. Rep. NA 72.50, Royal Inst Technology, Stockholm, 1972.
	7	POLAK, S.J. Prorate commumcatlon. ISA, Gebouw VM, Phfllps, Emdhoven, The Netherlands.
	8	RICHTMEYER, R.D., AND MORTON, K.W D~fference Methods for Initial Value Problems. Intersclence, New York, 1967.
	9	RYDER, B. G The PFORT verifier. Softw Prac. Exper 4 (1974), 359-378.
	10	SHAMPINE, L., AND GORDON, M K. Computer solutton of ordinary d~fferent~al equattons The Intt~al Value Problem, W H. Freeman, San Francisco, 1975.
	11	Richard F. Sincovec , Niel K. Madsen, Software for Nonlinear Partial Differential Equations, ACM Transactions on Mathematical Software (TOMS), v.1 n.3, p.232-260, Sept. 1975 [doi>10.1145/355644.355649]
	12	TE RIELE, H.J J., ED Colloquium numemeke programmatuur (Dutch), MC syllabus 29.2, Mathematlsch Centrum, Amsterdam, 1977.
	13	VAN DER HOUWEN, P J Constructmn of integration Formulas for In~ttal Value Problems. North-Holland, Amsterdam, 1976.
	14	VERWER, J.G. A class of stabilized three-step Runge-Kutta methods for the numerical integrauon of parabohc equations J Computat. Appl. Math 3 (1977), 155-166.
	15	J. G. Verwer, Algorithm 553: M3RK, An Explicit Time Integrator for Semidiscrete Parabolic Equations [D3], ACM Transactions on Mathematical Software (TOMS), v.6 n.2, p.236-239, June 1980 [doi>10.1145/355887.355897]
	16	VERWER, J.G. Mulhpoint multlstep Runge-Kutta methods I: On a class of two-step methods for parabolic equations. Rep NW30/76, Mathematisch Centrum, Amsterdam, 1976.
	17	VERWER, J.G. Mulhpomt multistep Runge-Kutta methods ii: The construction of a class of stabilized three-step methods for parabohc equations Rep. NW31/76, Mathematisch Centrum, Amsterdam, 1976.

CITED BY 2

	J. G. Verwer, Algorithm 553: M3RK, An Explicit Time Integrator for Semidiscrete Parabolic Equations [D3], ACM Transactions on Mathematical Software (TOMS), v.6 n.2, p.236-239, June 1980
	H. N. Najm , O. M. Knio, Modeling Low Mach Number Reacting Flow with Detailed Chemistry and Transport, Journal of Scientific Computing, v.25 n.1, p.263-287, October 2005