A collocation/quadrature-based Sturm-Liouville problem solver

Applied Mathematics and Computation

Volumn 110, Issue 2-3, 2000, Pages 205-223

  Adomaitis, Raymond A ^a   Lin, Yi Hung ^a  

^a UNIVERSITY OF MARYLAND   (United States)

Author keywords

Collocation; Computational methods; Eigenfunction expansions; Quadrature; Sturm Liouville problems

Indexed keywords

EID: 0039931243     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0096-3003(99)00065-X     Document Type: Article

References (22)

1. Bangia A.K., Batcho P.F., Kevrekidis I.G., Karniadakis G.Em. Unsteady two-dimensional flows in complex geometries: Comparative bifurcation studies with global eigenfunction expansions. SIAM J. Sci. Comput. 18(3):1997;775-805.
2. Pruess S., Fulton C.T. Mathematical software for Sturm-Liouville problems. ACM Trans. Math. Software. 19(3):1993;360-376.
3. D. Hinton, P.W. Schaefer, (Eds.), Spectral Theory and Computational Methods of Sturm-Liouville Problems, Lecture Notes in Pure and Applied Mathematics 191 Marcel Dekker, New York, 1997.
4. J.D. Pryce, Numerical Solution of Sturm-Liouville Problems, Oxford University Press, Oxford, UK, 1994.
5. Vanden Berghe G., Van Daele M., De Meyer H. A modified difference scheme for periodic and semiperiodic Sturm-Liouville problems. Appl. Num. Math. 18:1995;69-78.
6. A.H. Stroud, Numerical Quadrature and the Solution of Ordinary Differential Equations, Applied Mathematical Science Series, Vol. 10, Springer-Verlag, New York, 1974.
7. Villadsen J., Stewart W.E. Solution of boundary-value problems by orthogonal collocation. Chem. Engng Sci. 22:1967;1483-1501.
8. Michelsen M.L., Villadsen J. A convenient computational procedure for collocation constants. Chem. Eng. J. 4:1972;64-68.
9. J. Villadsen, M.L. Michelsen, Solution of Differential Equation Models by Polynomial Approximation, Int. Series in Phys. and Chem. Engng Sci. Prentice-Hall, Englewood Cliffs, NJ, 1978.
10. Y.-h. Lin, H.-Y. Chang, R.A. Adomaitis, MWRtools: A library for weighted residual methods, ISR TR 98-24, 1998.
11. R.G. Rice, D.D. Do, Applied Mathematics and Modeling for Chemical Engineers, Wiley, New York, 1995.
12. R.A. Adomaitis, Y.-h. Lin, A technique for accurate collocation residual calculations, Chem. Engng J., 71 (1998) 127-134, also ISR TR 98-6, 1998.
13. Joyce D.C. Survey of extrapolation processes in numerical analysis. SIAM Rev. 13:1971;435-490.
14. M. Jakob, Heat Transfer, Wiley, New York, 1949.
15. W.H. Ray, Advanced Process Control, Chemical Engineering Series, McGraw-Hill, New York, 1981.
16. Lee J.-Y., Greengard L. A fast adaptive numerical method for stiff two-point boundary-value problems. SIAM J. Sci. Comput. 18(2):1997;403-429.
17. Gottlieb D., Shu C.-W. On the Gibbs phenomenon and its resolution. SIAM Rev. 39(4):1997;644-668.
18. H.-Y. Chang, R.A. Adomaitis, Analysis of heat transfer in a chemical vapor deposition reactor: An eigenfunction expansion solution approach, Int. J. Heat and Fluid Flow, 20 (1999) 74-83, also ISR TR 97-84, 1997.
19. H.Y. Chang, R.A. Adomaitis, Model reduction for a tungsten chemical vapor deposition system, Proc. DYCOPS-5 Corfu, Greece, 35-40, also ISR TR 98-28, 1998.
20. H.-Y., Chang, Y.-h. Lin, R.A. Adomaitis, Statistically-determined trial functions for RTCVD system model reduction and simulation, AIChE Annual Meeting Los Angeles, 1997.
21. Shvartsman S.Y., Kevrekidis I.G. Non-linear model reduction for feedback control of distributed parameter systems: A computer-assisted study. AIChE J. 44:1998;1579.
22. R.A. Adomaitis, Software and other teaching tools applied to modeling and analysis of distributed parameter systems, Proc. ASEE Regional Conf., Wilmington, DE, Oct. 1997.