A novel approach for the solution of a class of singular boundary value problems arising in physiology

Mathematical and Computer Modelling

Volumn 52, Issue 3-4, 2010, Pages 626-636

  Khuri, S A ^a   Sayfy, A ^a  

^a AMERICAN UNIVERSITY OF SHARJAH   (United Arab Emirates)

Author keywords

Cubic B spline collocation; Decomposition method; Physiology applications; Singular boundary value problems

Indexed keywords

APPROXIMATE SOLUTION; B-SPLINE; CUBIC B -SPLINE; DECOMPOSITION METHODS; EXACT SOLUTION; INTEGRAL OPERATORS; MODIFIED DECOMPOSITION METHOD; NEW APPROACHES; NUMERICAL SOLUTION; PHYSIOLOGY APPLICATIONS; SINGULAR BOUNDARY VALUE PROBLEMS; SINGULAR POINTS; SUBINTERVALS;

BOUNDARY VALUE PROBLEMS; NUMERICAL ANALYSIS; OPERATIONS RESEARCH; ORDINARY DIFFERENTIAL EQUATIONS; SPLINES;

SINGULAR VALUE DECOMPOSITION;

EID: 77954863371     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mcm.2010.04.009     Document Type: Article

References (21)

1. Lin HS. Oxygen diffusion in a spherical cell with nonlinear oxygen uptake kinetics. J. Theor. Biol. 1976, 60:449-457.
2. McElwain DLS. A re-examination of oxygen diffusion in a spherical cell with Michaelis-Menten oxygen uptake kinetics. J. Theor. Biol. 1978, 71:255-263.
3. Flesch U. The distribution of heat sources in the human head: a theoretical consideration. Journal of Theor. Biol. 1975, 54:285-287.
4. Garner J.B., Shivaji R. Diffusion problems with mixed nonlinear boundary condition. Journal of Math. Anal. Appl. 1990, 148:422-430.
5. Ravi Kanth A.S.V., Bhattacharya Vishnu Cubic spline for a class of non-linear singular boundary value problems arising in physiology. Appl. Math. Comput. 2006, 174(1):768-774.
6. Pandey R.K., Singh Arvind K. On the convergence of a finite difference method for a class of singular boundary value problems arising in physiology. J. Comput. Appl. Math. 2004, 166:553-564.
7. Caglar Hikmet, Caglar Nazan, Ozer Mehmet B-spline solution of non-linear singular boundary value problems arising in physiology. Chaos Solitons Fractals 2009, 39:1232-1237.
8. Asaithambi N.S., Garner J.B. Pointwise solution bounds for a class of singular diffusion problems in physiology. Appl. Math. Comput. 1989, 30(3):215-222.
9. Gustaffsson B. A numerical method for solving singular boundary value problems. Numer. Math. 1973, 21:328-344.
10. Ravi Kanth A.S.V., Reddy Y.N. The method of inner boundary condition for singular boundary value problems. Appl. Math. Comput. 2003, 139(2-3):429-436.
11. Ravi Kanth A.S.V., Reddy Y.N. A numerical method for singular two point boundary value problems via Chebyshev economizition. Appl. Math. Comput. 2003, 146(2-3):691-700.
12. Hiltmann P., Lory P. On oxygen diffusion in a spherical cell with Michaelis-Menten oxygen uptake kinetics. Bull. Math. Biol. 1983, 45:661-664.
13. Adomian G. Solving Frontier Problems of Physics: The Decomposition Method 1994, Kluwer.
14. Deeba E., Khuri S.A. Nonlinear equations. Wiley Encyclopedia of Electrical and Electronics Engineering 1999, vol. 14:562-570. John Wiley & Sons, NewYork.
15. Deeba E.Y., Khuri S.A. A decomposition method for solving the nonlinear Klein-Gordon equation. J. Comput. Phys. 1996, 124:442-448.
16. Khuri S.A. A new approach to Bratu's problem. Appl. Math. Comput. 2004, 147:131-136.
17. Khuri S.A. A numerical algorithm for solving the Troesch's problem. Int. J. Comput. Math. 2003, 80(4):493-498.
18. Khuri S.A. On the solution of coupled H-like equations of Chandrasekhar. Appl. Math. Comput. 2002, 133(2-3):479-485.
19. Khuri S.A. An alternative solution algorithm for the nonlinear generalized Emden-Fowler equation. Int. J. Nonlinear Sci. Numeri. Simul. 2001, 2:299-302.
20. Khuri S.A. On the decomposition method for the approximate solution of nonlinear ordinary differential equations. Int. J. Math. Ed. Science Tech. 2001, 32(4):525-539.
21. Khuri S.A. A Laplace decomposition algorithm applied to a class of nonlinear differential equations. J. Appl. Math. 2001, 1(4):141-155.