Differential quadrature method for singularly perturbed two-point boundary value problems

Journal of Applied Sciences

Volumn 8, Issue 6, 2008, Pages 1091-1096

  Sari, M ^a  

^a PAMUKKALE UNIVERSITY   (Turkey)

Author keywords

Boundary layer; Differential quadrature method; Ordinary differential equation; Singular perturbation; Two point boundary value problem

Indexed keywords

BOUNDARY LAYERS; DIFFERENTIAL EQUATIONS; DIFFERENTIATION (CALCULUS); NUMERICAL METHODS; ORDINARY DIFFERENTIAL EQUATIONS; PERTURBATION TECHNIQUES; PREDICTIVE CONTROL SYSTEMS; SPACE RENDEZVOUS;

DIFFERENTIAL QUADRATURE METHODS; EXACT SOLUTION; HIGH-ACCURACY; NUMBER OF GRIDS; NUMERICAL SOLUTION; SINGULAR PERTURBATIONS; SINGULARLY PERTURBED; TWO POINT BOUNDARY VALUE PROBLEMS;

BOUNDARY VALUE PROBLEMS;

EID: 41949083257     PISSN: 18125654     EISSN: 18125662     Source Type: Journal    
DOI: 10.3923/jas.2008.1091.1096     Document Type: Article

References (23)

1. Bellman, R., B.G. Kashef and J. Casti, 1972. Differential quadrature: A technique for the rapid solution of nonlinear partial differential equations. J. Comput. Phys., 10 (1): 40-52.
2. Bender, C.M. and S.A. Orszag, 1978. Advanced Mathematical Methods for Scientist and Engineers. McGraw-Hill, New York.
3. Berger. A.E., J.M. Solomon and M. Ciment. 1981. An analysis of a uniformly accurate difference method for a singular perturbation problem. Math. Comput., 37 (155): 79-94.
4. Cheri, J., 1997. The p-version of the finite element method for a singularly perturbed boundary value problem. J. Comput. Applied Math., 84 (1): 119-135.
5. Cheri, C.L. and Y.C. Liu, 1998. Solution of two-point boundary-value problems using the differential transformation method. J. Optimiz. Theory Applied, 99 (1): 23-35.
6. Chin, R.C. and R. Krasny, 1983. A hybrid asymtotic finite element method for stiff two-point boundary value problems. SIAM. J. Sci. Stat. Comput., 4 (2): 229-243.
7. Flaherty, J.E. and W. Mathon, 1980. Collocation with polinomial and tension splines for singularly-perturbed boundary value problems. SIAM. J. Sci. Stat. Comput., 1 (2): 260-289.
8. Ilicasu, F.O. and D.H. Schultz, 2004. Higher-Order finite difference techniques for linear singular perturbation boundary value problems. Comput. Math. Applied, 47 (2-3): 391-417.
9. Jain, M.K. and T. Aziz, 1983. Numerical solution of stiff and convection diffusion equations using adaptive spline function approximation. Applied Math. Model., 7 (1): 57-62.
10. Kadalbajoo, M.K. and K.C. Patidar, 2003a. Exponentially fitted spline in compression for the numerical solution of singular perturbation problems. Comput. Math. Applied, 46 (5-6): 751-767.
11. Kadalbajoo, M.K. and K. C. Patidar, 2003b. Variable mesh spline in compression for the numerical solution of singular perturbation problems. Int. J. Comput. Math., 80 (1): 83-93.
12. Kellogg, R.B. and A. Tsan, 1978. Analysis of some difference approximations for a singular perturbation problem without turning points. Math. Comput., 32 (144): 1025-1039.
13. Khan, A., I. Khan, T. Aziz and M. Stojanovic, 2004. A variable-mesh approximation method for singularly perturbed boundary value problems using cubic spline in tension. Int. J. Comput. Math., 81 (12): 1513-1518.
14. Liu, W. and T. Tang, 2001. Error analysis for a Galerkin-spectral method with coordinate transformation for solving singularly perturbed problems. Applied Numer. Math., 38 (3): 315-345.
15. Reddy, Y.N. and K.A. Reddy, 2002. Numerical integration method for general singularly perturbed two point boundary value problems. Applied Math Comput., 133 (2-3): 351-373.
16. Sakai, M. and R.A. Usmani, 1989. A class of simple exponential B-splines and their applications to numerical solution to singular perturbation problems. Numer. Math., 55 (5): 493-500.
17. Schatz, A.H. and L.B. Wahlbin, 1983. On the finite element method for singularly perturbed reaction diffusion problems in two and one dimension. Math. Comput., 40 (161): 47-89.
18. Shu, C., 1991. Generalized differential-integral quadrature and application to the simulation of incompressible viscous flows including parallel computation. Ph.D Thesis, University of Glasgow, UK.
19. Shu, C. and B.E. Richards, 1992. Application of generalized differential quadrature to solve two-dimensional incompressible Navier-Stokes equations. Int. J. Numer. Meth. Fl., 15 (7): 791-798.
20. Shu, C., 2000. Differential Quadrature and Its Application in Engineering. Springer-Verlag, London.
21. Stojanovic, M., 1996. Spline difference methods for a singular perturbation problem. Applied Numer. Math., 21 (3): 321-333.
22. Stynes, M. and E. O'Riordan, 1986. A finile element method for a singularly perturbed boundary value problem. Numer. Math., 50 (1): 1-15.
23. Yücel, U., 2006. Approximations of Sturm-Liouville eigenvalues using differential quadrature (DQ) method. J. Comput. Applied Math., 192 (2): 310-319.