An algorithm for solving singular perturbation problems with mechanization

Applied Mathematics and Computation

Volumn 188, Issue 1, 2007, Pages 286-302

  Habib, H M ^a   El Zahar, E R ^a  

^a MENOUFIA UNIVERSITY   (Egypt)

Author keywords

Algorithm; Finite difference method; matlab; Mechanization; Singular perturbation problems (SPP)

Indexed keywords

ALGORITHMS; BOOLEAN ALGEBRA; FINITE DIFFERENCE METHOD; MECHANIZATION; PROBLEM SOLVING;

MATHEMATICAL ANALYSIS; SINGULAR PERTURBATION PROBLEMS (SPP);

PERTURBATION TECHNIQUES;

EID: 34247876015     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2006.09.132     Document Type: Article

References (26)

1. Wu W. Basic principles of mechanical theorem proving in elementary geometries. J. Automat. Reasoning. 2 (1986) 221-252
2. Glimm J.G. Mathematical Sciences, Technology, and Economic Competitiveness (1992), National Academy Press, Washington, DC
3. Reddy Y.N., and Chakravarthy P.P. An initial-value approach for solving singular perturbed two-point boundary value problems. Appl. Math. Comput. 155 (2004) 95-110
4. Reddy Y.N., and Pramod Chakravarthy P. Numerical patching method for singularly perturbed two-point boundary value problems using cubic splines. Appl. Math. Comput. 149 (2005) 441-468
5. Suli E. Numerical Solution of Ordinary Differential Equations (2001), Oxford University
6. Ascher U., Mattheij R., and Russell R. Numerical Solution of Boundary Value Problems for Ordinary Differential Equations (1995), SIAM Press, Philadelphia
7. Roos H.-G., Stynes M., and Tobiska L. Numerical Methods for Singularly Perturbed Differential Equations (1996), Springer, New York
8. Fornberg B. Calculation of Weights in Finite Difference Formulas. SIAM, Rev. 40 (1998) 685-691
9. S. Wolfram, The numerical method of lines for partial differential equations. Available from: .
10. Burden R.L., and Faires J.D. Numerical Analysis. fourth ed. (1989), PWS-KENT, USA
11. Maron M.J. Numerical Analysis: A Practical Approach (1982), Macmillan Publishing Co., New York
12. Gilbert J.R., Moler C., and Schreiber R. Sparse Matrices In MATLAB: Design And implementation (1992), SIAM
13. Baltensperger R., and Trummer M.R. Spectral differencing with a twist. SIAM J. Sci. Comput. (2002)
14. Friendman A., Glimm J., and Lavery J. The Mathematical and Computational Sciences in Emerging Manufacturing Technogies and Management Practies (1992), SIAM pp. 62-63
15. Glimm J.G. Mathematical Sciences, Technology, and Economic Competitiveness (1992), National Academy Press, Washington, DC
16. Duffy D.J. Advanced Engineering Mathematics with MATLAB (2003), Chapman & Hall, New York
17. Ashino R., Nagase M., and Vaillancourt R. Behind and beyond the MATLAB ODE suite. J. Comput. Math. Appl. 40 (2000)
18. Shampine L.F., and Thompson S. Solving DDEs in MATLAB. Appl. Numer. Math. 37 (2001) 441-458
19. L.F. Shampine, M.W. Reichelt, and J.Kierzenka, Solving boundary value problems for ordinary differential equations in Matlab with bvp4c, 2000. Available from: .
20. Baglama J., Calvetti D., and Reichel L. Algorithm 827: irbleigs: A MATLAB program for computing a few eigenpairs of a large sparse Hermitian matrix. ACM Trans. Math. Soft. 29 (2003) 337-348
21. Zeng Z. Algorithm 835: MultRoot-a Matlab package for computing polynomial roots and multiplicities. ACM Trans. Math. Soft. 30 (2004) 218-236
22. VandeWouwera A., Saucez P., Schiesser W.E., and Thompson S. A MATLAB implementation of upwind finite differences and adaptive grids in the method of lines. Comput. Appl. Math. 183 (2005) 245-258
23. Z. Li, W. Wang, Mechanization for solving SPP by reducing order method, Appl. Math. Comput., in press.
24. Bender C.M., and Orszag S.A. Advanced Mathematical Methods for Scientists and Engineers (1978), McGraw-Hill, New York
25. Kevorkian J., and Cole J.D. Perturbation Methods in Applied Mathematics (1981), Springer-Verlag, New York
26. O' Malley R.E. Introduction to Singular Perturbations (1974), Academic Press, New York