Algorithm 540: PDECOL, General Collocation Software for Partial Differential Equations [D3]

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Algorithm 540: PDECOL, General Collocation Software for Partial Differential Equations [D3]

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ACM Transactions on Mathematical Software (TOMS) archive
Volume 5 , Issue 3 (September 1979) table of contents

Pages: 326 - 351

Year of Publication: 1979

ISSN:0098-3500

Authors

N. K. Madsen	Lawrence Livermore Laboratory, Livermore, CA
R. F. Sincovec	Boeing Computer Services, Co., Energy Technology Applications, Mail Stop 9C-01, P.O. Box 24346, Seattle, WA

Publisher

ACM New York, NY, USA

Bibliometrics

Downloads (6 Weeks): 14, Downloads (12 Months): 129, Citation Count: 8

Additional Information:

appendices and supplements references cited by index terms collaborative colleagues peer to peer

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APPENDICES and SUPPLEMENTS

PDECOL (540.gz) (35 KB)

coupled systems of nonlinear partial differential equations in one space and one time dimension. The solution method uses finite element collocation based upon piecewise polynomials for spatial discretization. The time discretization is done by general-purpose software for ordinary initial value problems
Gams: I2a1a,I2a2

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	CURRY, H.B., AND SCHOENBERG, I.J. On Folya frequency functions IV: The fundamental splme functions and the~ \|irnlts. J. Anal Math. 17 (1966), 71-107.
	2	DEBOOR, C. On calculating with B-splines. J. Approx. Theory 6, 1 (July 1972), 50-62.
	3	DEBooR, C. Package for calculating with B-splines. SIAM J. Namer. Anal. 14, 3 (June 1977), 441-472.
	4	DzBooR, C., AN~ SWARTZ, B. Collocation at Gaussian points. SIAM j. Namer. Anal. 10, 4 (Sept. 1973), 582-606.
	5	C. William Gear, Numerical Initial Value Problems in Ordinary Differential Equations, Prentice Hall PTR, Upper Saddle River, NJ, 1971
	6	HINDMARSH, A.C. Preliminary documentation of GEARIB: Solution of implicit systems of ordinary differential equations with banded Jacobian. Rap. UCID-30130, Lawrence Livermore Lab., Llvermore, Calif, 1976.
	7	MADSEN, N.K, AND SINCOVEC, R.F. The numerical method of lines for the solution of nonlinear partial differential equations, in Computatmnal Methods in Nonlinear Mechanics, J.T. Oden et al., Eds., Texas Inshtute for Computational Mechanics, Austin, Tex., 1974, pp. 371-380.
	8	MADSEN, N.K, AND SINCOVEC, R.F. PDEPACK: A new tool for simulation. Proc. 1975 Summer Computer Simulation Conf., San Francisco, Calif., July 1975, pp. 144-149. (~ 1975 by the Simulation Councils, Inc., P.O. Box 2228, La Jolla, Calif. 92037 )
	9	MADSEN, N.K., AND S1NCOVEC, R.F. General software for partial differential equations. In Numerwal Methods for D~fferent~al Systems, L. Lapldus and W E. Schiesser, Eds., Academic Press, New York, 1976, pp. 229-242.
	10	SINCOVEC, R.F. On the relative efficiency of h:gher order collocation methods for solving twopoint boundary value problems. SIAM J Numer. Anal. 14, 1 (March 1977), 112-123.
	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	Richard F. Sincovec , Niel K. Madsen, Algorithm 494: PDEONE, Solutions of Systems of Partial Differential Equations [D3], ACM Transactions on Mathematical Software (TOMS), v.1 n.3, p.261-263, Sept. 1975 [doi>10.1145/355644.355650]
	13	SWAnTZ, B.K., AND VARGA, R.S. Error bounds for spline and L-spline interpolation. J. Approx Theory 6, 1 (July 1972), 6-49

CITED BY 8

	P. Keast , P. H. Muir, Algorithm 688; EPDCOL: a more efficient PDECOL code, ACM Transactions on Mathematical Software (TOMS), v.17 n.2, p.153-166, June 1991
	David K. Melgaard , Richard F. Sincovec, General Software for Two-Dimensional Nonlinear Partial Differential Equations, ACM Transactions on Mathematical Software (TOMS), v.7 n.1, p.106-125, March 1981
	R. Wang , P. Keast , P. Muir, BACOL: B-spline adaptive collocation software for 1-D parabolic PDEs, ACM Transactions on Mathematical Software (TOMS), v.30 n.4, p.454-470, December 2004
	M. Berzins , P. M. Dew, Algorithm 690; Chebyshev polynomial software for elliptic-parabolic systems of PDEs, ACM Transactions on Mathematical Software (TOMS), v.17 n.2, p.178-206, June 1991
	R. Wang , P. Keast , P. Muir, A high-order global spatially adaptive collocation method for 1-D parabolic PDEs, Applied Numerical Mathematics, v.50 n.2, p.239-260, August 2004
	R. Wang , P. Keast , P. H. Muir, Algorithm 874: BACOLR—spatial and temporal error control software for PDEs based on high-order adaptive collocation, ACM Transactions on Mathematical Software (TOMS), v.34 n.3, p.1-28, May 2008
	Rong Wang , Patrick Keast , Paul Muir, A comparison of adaptive software for 1D parabolic PDEs, Journal of Computational and Applied Mathematics, v.169 n.1, p.127-150, 1 August 2004
	E. N. Houstis , J. R. Rice , S. Weerawarana , A. C. Catlin , P. Papachiou , K.-Y. Wang , M. Gaitatzes, PELLPACK: a problem-solving environment for PDE-based applications on multicomputer platforms, ACM Transactions on Mathematical Software (TOMS), v.24 n.1, p.30-73, March 1998