Collocation Software for Boundary-Value ODEs

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Collocation Software for Boundary-Value ODEs

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ACM Transactions on Mathematical Software (TOMS) archive
Volume 7 , Issue 2 (June 1981) table of contents

Pages: 209 - 222

Year of Publication: 1981

ISSN:0098-3500

Authors

U. Ascher	Department of Computer Science, University of British Columbia, Vancouver, B.C. V6T 1W5, Canada
J. Christiansen	Mathematics Department, Simon Fraser University, Burnaby, B.C. V5A 1S6, Canada
R. D. Russell	Mathematics Department, Simon Fraser University, Burnaby, B.C. V5A 1S6, Canada

Publisher

ACM New York, NY, USA

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Downloads (6 Weeks): 8, Downloads (12 Months): 120, Citation Count: 14

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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	ASCHER, U. Solving boundary value problems with a spline-collocatlon code. J Comput. Phys. 34 (1980), 401-413.
	2	Uri Ascher , J. Christiansen , R. D. Russell, A Collocation Solver for Mixed Order Systems of BVP''s, University of British Columbia, Vancouver, BC, Canada, 1977
	3	Uri M. Ascher , J. Christiansen , Robert D. Russell, COLSYS - - A Collocation Code for Boundary - Value Problems, Proceedings of a Working Conference on Codes for Boundary-Value Problems in Ordinary Differential Equations, p.164-185, May 14-17, 1978
	4	Uri Ascher , R. D. Russell, Evaluation of B-splines for Solving Systems of Boundary Value Problems, University of British Columbia, Vancouver, BC, Canada, 1977
	4a	ASCHER, U., AND RUSSELL, R.D. Reformation of boundary value problems in "standard" form. SIAM Rev 23 (April 1981).
	5	BULIRSCH, R., STOER, J, AND DEUFLHARD, P. Numerical solution of nonlinear two-point boundary value problems I. Numer. Math. Handbook Ser~es Approximation (1976).
	5a	CODES FOR BOUNDARY VALUE PROBLEMS B. Childs et al (Eds.), Lecture Notes in Computer Science 76, Springer-Verlag, New York, 1979.
	6	DE BOOR, C. On calculating with B-splines. J. Approx. Theory 6 (1972), 50-62
	7	Carl de Boor , Richard Weiss, SOLVEBLOK: A Package for Solving Almost Block Diagonal Linear Systems, ACM Transactions on Mathematical Software (TOMS), v.6 n.1, p.80-87, March 1980 [doi>10.1145/355873.355880]
	8	DEUFLHARD, P. A stepsize control for continuation methods with special application to multiple shooting techniques. TUM-Math-7627, Munchen, Germany, 1976.
	9	DIEKOFF, H.J., Lo~, P., OBERLE, H.J., PESCH, H.J., RENTROP, P., AND SEYDEL, R. Comparing routines for the numerical solution of initial value problems of ordinary differential equations in multiple shooting. Numer. Math. 27 (1977), 449-469.
	10	GAWAIN, T.H., AND BALL, R.E. Improved finite difference formulas for boundary value problems. Int. J. Numer. Meth. Eng. 12 (1978), 1151-1160.
	11	GLADWELL, I. Shooting codes in the NAG library. In B. Chdds et al. (Eds.), Lecture Notes m Computer Science 76, Sprmger-Verlag, New York, 1979.
	12	James F. Holt, Numerical solution of nonlinear two-point boundary problems by finite difference methods, Communications of the ACM, v.7 n.6, June 1964 [doi>10.1145/512274.512291]
	13	LENTINI, M., AND PEREYRA, V An adaptive fimte difference solver for nonlinear two point boundary problems with mild boundary layers. SIAM J. Numer Anal 14 (1977), 91-111.
	14	Victor Pereyra, PASVA3: An Adaptive Finite Difference Fortran Program for First Order Nonlinear, Ordinary Boundary Problems, Proceedings of a Working Conference on Codes for Boundary-Value Problems in Ordinary Differential Equations, p.67-88, May 14-17, 1978
	15	SCOTT, M.L., AND WATTS, H.A. Computational solutions of linear two-point boundary problems via orthonormalization. SIAM J. Numer. Anal. 14 (1977), 40-70.
	16	Melvin R. Scott , H. A. Watts, Superposition, Orthonormalization, Quasilinearization and Two-Point Boundary - Value Problems, Proceedings of a Working Conference on Codes for Boundary-Value Problems in Ordinary Differential Equations, p.109-121, May 14-17, 1978
	17	WAN, F. The dimpling of spherical caps. Tech. Rep. 78-6, Inst. of Applied Mathematics, Univ. British Columbia, Vancouver, Canada, 1978.

CITED BY 14

	J.-Fr. Hake, Remark on “Algorithm 569: COLSYS: Collocation Software for Boundary-Value ODEs [D2]”, ACM Transactions on Mathematical Software (TOMS), v.12 n.3, p.283-284, Sept. 1986
	U. Ascher , J. Christiansen , R. D. Russell, Algorithm 569: COLSYS: Collocation Software for Boundary-Value ODEs [D2], ACM Transactions on Mathematical Software (TOMS), v.7 n.2, p.223-229, June 1981
	J. C. Diaz , G. Fairweather , P. Keast, FORTRAN Packages for Solving Certain Almost Block Diagonal Linear Systems by Modified Alternate Row and Column Elimination, ACM Transactions on Mathematical Software (TOMS), v.9 n.3, p.358-375, Sept. 1983
	Gouad Majaess , Patrick Keast , Graeme Fairweather , Karin R. Bennett, The solution of almost block diagonal linear systems arising in spline collocation at Gaussian points with monomial basis functions, ACM Transactions on Mathematical Software (TOMS), v.18 n.2, p.193-204, June 1992
	Wayne H. Enright , Ramanan Sivasothinathan, Superconvergent interpolants for collocation methods applied to mixed-order BVODEs, ACM Transactions on Mathematical Software (TOMS), v.26 n.3, p.323-351, Sept. 2000
	J. R. Cash , G. Moore , R. W. Wright, An automatic continuation strategy for the solution of singularly perturbed nonlinear boundary value problems, ACM Transactions on Mathematical Software (TOMS), v.27 n.2, p.245-266, June 2001
	Dieter Kraft, Algorithm 733; TOMP—Fortran modules for optimal control calculations, ACM Transactions on Mathematical Software (TOMS), v.20 n.3, p.262-281, Sept. 1994
	C. Budd , O. Koch , E. Weinmüller, Computation of Self-similar Solution Profiles for the Nonlinear Schrödinger Equation, Computing, v.77 n.4, p.335-346, June 2006
	P. H. Muir , R. N. Pancer , K. R. Jackson, PMIRKDC: a parallel mono-implicit Runge--Kutta code with defect control for boundary value ODEs, Parallel Computing, v.29 n.6, p.711-741, June 2003
	T. L. Boyadjiev , M. D. Todorov , P. P. Fiziev , S. S. Yazadjiev, A numerical algorithm for modelling of boson-fermion stars in dilatonic gravity, Journal of Computational and Applied Mathematics, v.145 n.1, p.113-131, 1 August 2002
	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
	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
	W. F. Finden, Higher order approximations using interpolation applied to collocation solutions of two-point boundary value problems, Journal of Computational and Applied Mathematics, v.206 n.1, p.99-115, September, 2007
	M. Benosman , F. Boyer , G. Le Vey , D. Primault, Flexible Links Manipulators: from Modelling to Control, Journal of Intelligent and Robotic Systems, v.34 n.4, p.381-414, August 2002