High-Order Finite-Difference Techniques for Linear Singular Perturbation Boundary Value Problems

Computers and Mathematics with Applications

Volumn 47, Issue 2-3, 2004, Pages 391-417

  Ilicasu, F O ^a   Schultz, D H ^b  

^a ROWAN UNIVERSITY   (United States)

^b UNIVERSITY OF WISCONSIN MILWAUKEE   (United States)

Author keywords

Boundary layers; Finite differences; Singular perturbation problems; Viscosity

Indexed keywords

APPROXIMATION THEORY; BOUNDARY LAYERS; CONVERGENCE OF NUMERICAL METHODS; DIFFERENTIAL EQUATIONS; DIFFUSION; ERROR ANALYSIS; FINITE DIFFERENCE METHOD; PERTURBATION TECHNIQUES; PROBLEM SOLVING; VISCOSITY;

FINITE DIFFERENCES; SINGULAR PERTURBATION PROBLEMS;

BOUNDARY VALUE PROBLEMS;

EID: 1242352541     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0898-1221(04)90033-8     Document Type: Article

References (16)

1. S.A. Lomov, Introduction to the General Theory of Singular Perturbations, American Mathematical Society, (1992).
2. A. Segal, Aspects of numerical methods for elliptic singular perturbation problems, SIAM J. Sci. Stat. Comput. 3 (3), 327-349, (1982).
3. P.W. Hemker, A Numerical Study of Stiff Two-Point Boundary Problems, Mathematisch Centrum, Amsterdam, (1977).
4. I. Christie, D.F. Griffiths, A.R. Mitchell and O.C. Zienkiewicz, Finite element methods for second order equations with significant first derivatives, Int. J. Num. Methods Eng. 10, 1389-1396, (1976).
5. O. Axelsson and I. Gustafsson, A modified upwind gradient scheme for connective transport equations, and the use of a conjugate method for the solution of nonsymmetric systems of equations, J. Inst. Math. Appl. 23, 321-337, (1979).
6. S.K. Dekema and D.H. Schultz, High-order methods for differential equations with large first-derivative terms, Int. J. Num. Methods Fluids 10, 259-284, (1990).
7. J.Y. Choo and D.H. Schultz, Stable high order methods for differential equations with small coefficients for the second order terms, Computers Math. Applic. 25 (1), 105-123, (1993).
8. A.M. Il'in, Differencing scheme for a differential equation with a small parameter affecting the highest derivative, Math. Notes Acad. Sc. USSR 6, 596-602, (1969).
9. J.J. Miller, E. O'Riordan and G.I. Shishkin, Fitted Numerical Methods for Singular Perturbation Problems, World Scientific, (1996).
10. T.N. Varner and S.R. Choudhury, Nonstandard difference schemes for singular perturbation problems revisited, Applied Mathematics and Computation 92, 101-123, (1998).
11. H.B. Keller, Numerical Methods for Two-Point Boundary-Value Problems, Blaisdell, (1968).
12. D. Greenspan and V. Casulli, Numerical Analysis for Applied Mathematics, Science, and Engineering, Addison-Wesley, (1988).
13. P. Linz, Theoretical Numerical Analysis, John Wiley and Sons, (1979).
14. O. Axelsson, Iterative Solution Methods, Cambridge University Press, (1996).
15. S.H. Leventhal, An operator compact implicit method of exponential type, J. Comput. Physics 46, 138-165, (1982).
16. H.B. Keller, Numerical Solution of Two Point Boundary Value Problems, Volume 24, Regional Conference Series in Applied Mathematics, SIAM, (1976).