'Shooting method' for singular perturbation problems arising in chemical reactor theory

International Journal of Computer Mathematics

Volumn 70, Issue 2, 1998, Pages 251-262

  Natesan, S ^a   Ramanujam, N ^a  

^a BHARATHIDASAN UNIVERSITY   (India)

Author keywords

Asymptotic expansion; Boundary layer; Exponentially fitted difference scheme; Parallel computation; Singular perturbation; Small parameter

Indexed keywords

BOUNDARY LAYERS; CHEMICAL REACTORS; COMPUTATION THEORY; FINITE DIFFERENCE METHOD; INITIAL VALUE PROBLEMS; ORDINARY DIFFERENTIAL EQUATIONS; PARALLEL ARCHITECTURES;

ASYMPTOTIC EXPANSION; DIFFERENCE SCHEMES; PARALLEL COMPUTATION; SINGULAR PERTURBATIONS; SMALL PARAMETER;

NUMERICAL METHODS;

EID: 0005237085     PISSN: 00207160     EISSN: None     Source Type: Journal    
DOI: 10.1080/00207169808804750     Document Type: Article

References (15)

1. O'Malley, R. E. (1974). Introduction to singular perturbations. Academic Press, New York.
2. Baxley, J. V. (1977). On singular perturbation of nonlinear two-point boundary value problems, Czechoslovak Mathematical Journal, 27(102), 363 - 377.
3. Cohen, D. S. (1972). Multiple solutions of singular perturbation problems, SIAM J. Math. Anal., 3, 72 - 82.
4. Cohen, D. S. (1973). Multiple stable solutions of nonlinear boundary value problems arising in chemical reactor theory, SIAM J Math Anal., 20, 1 - 13.
5. Kadalbajoo, M. K. and Reddy, Y. N. (1989). Asymptotic and numerical analysis of singular perturbation problems: A survey, Appl. Math. Comput., 30, 223 - 259.
6. Roberts, S M. (1979). A boundary value technique for singular perturbation problems, J. Math. Anal. Apply., 87, 489 - 508.
7. Jayakumar, J. and Ramanujam, N. (1994). A numerical method for singular perturbation problems arising in chemical reactor theory, Comput. Math. Applic., 27(5), 83 - 99.
8. Doolen, E. P., Miller, J. J. H. and Schilders, W. H. A. (1980). Uniform numerical methods for problems with initial and boundary layers, Boole Press, Dublin, Ireland.
9. Vercelj, V., Adzic, N. and Uzelac, Z. (1991). A numerical-asymptotic solution for singular perturbation problems, Intern. J. Computer Math., 39, 229 - 238.
10. Ramanujam, N. and Srivastava, U. N. (1980). Singularly perturbed initial value problems for problems for nonlinear differential system, Indian J. Pure Appl. Math., 11, 98 - 113.
11. Krishnamurthy, E. V. and Sen, S. K. (1986). Numerical Algorithms, Affiliated East West Press Ltd., New Delhi.
12. Chang, K. W. and Howes, F. A. (1984). Nonlinear singular perturbation phenomena: Theory and Applications, Springer Verlag, New York.
13. O'Malley, R. E. (1991). Singular perturbation methods for ordinary differential equations, Springer Verlag, New York.
14. Hemker, P. W. (1977). A numerical study of stiff two-point boundary value problems, Mathematics Centre, Amsterdam, Holland.
15. Dorr, F. W., Parter, S. V. and Shampine, L. F. (1973). Application of the maximum principle to singular perturbation problems, SIAM Review, 15(1), 43 - 88.