REFERENCES
[1] M. Abukhaled, S. A. Khuri and A. Sayfy, A numerical approach for solving a
class of singular boundary value problems arising in physiology, Int. J. Numer. Anal. Model., 8:353–363, 2011.
[2] J. A. Adam, A simplified mathematical model of tumor growth, Math. Biosci., 81:229–244, 1986.
[3] R. P. Agarwal and Y. M. Chow, Finite difference methods for boundary value
problems for differential equations with deviating arguments, Comput. Math.
Appl., 12:1143–1153, 1986.
[4] R. P. Agarwal, Boundary Value Problems For Higher-Order Differential Equations,
World Scientific, Singapore, 1986.
[5] N. Anderson and A. M. Arthurs, Analytical diffusion in a spherical cell with
michaelis-menten oxygen uptake kinetics, Bull. Math. Biol., 47:145–153, 1983.
[6] N. S. Asaithambi and J. B. Garner, Pointwise solution bounds for a class of
singular diffusion problems in physiology, Appl. Math. Comput., 30:215–222, 1989.
[7] N. C¸ a˘glar and H. C¸ a˘glar, B-spline solution of singular boundary value problems,
Appl. Math. Comput., 182:1509–1513, 2006.
[8] H. C¸ a˘glar, N. C¸ a˘glar and M. Ozer, B-spline solution of non-linear singular bound- ¨
ary value problems arising in physiology, Chaos Solutions and Fractals, 39:1232– 1237, 2009.
[9] H. C¸ a˘glar, C. Akkoyunlu, N. C¸ a˘glar and D. Dundar, The numerical solution of
the singular two-point boundary value problems by using non-polynomial spline
functions, Proceedings of the 9th WSEAS Int. Conference on Applied Computer
And Applied Computational Science. ISSN: 1790-5117, ISBN: 978-960-474-173- 1.
[10] M. M. Chawla and C. P. Katti, Finite difference methods and their convergence
for a class of singular two point boundary value problem, Numer. Math., 39:341– 350, 1982.
[11] M. M. Chawla, S. McKee and G. Shaw, Order h
2 method for a singular two point
boundary value problem, BIT., 26:318–326, 1986.
[12] M. M. Chawla and R. Subramanian, A new spline method for singular two point
boundary value problems, Int. J. Comput. Math., 24:291–310, 1988.
[13] M. M. Chawla, R. Subramanian and H. Sathi, A fourth order method for a
singular two point boundary value problem, BIT., 28:88–97, 1988.
[14] A. M. Cohen and D. E. Jones, A note on the numerical solution of some singular
second order differential equations, J. Inst. Math. Appl., 13:379–384, 1974.
[15] M. G. Cui and F. Z. Geng, Solving singular two-point boundary value problem
in reproducing kernel space, J. Comput. Appl. Math., 205:6–15, 2007.
[16] E. P. Doolan, J. J. H. Miller and W. H. A. Schilders, Uniform Numerical Methods
for Problems With Initial and Boundary Layers, Boole Press, Dublin, 1980.
[17] R. C. Duggan and A. M. Goodman, Point wise bounds for a nonlinear heat
conduction model of the human head, Bull. Math. Biol., 48:229–236, 1986.
[18] M. El-Gamel and A. Zayed, A comparison between the Wavelet-Galerkin and the
Sinc-Galerkin methods in solving nonhomogeneous heat equations, in: Contemporary
Mathematics of the American Mathematical Society, in: Zuhair Nashed,
Otmar Scherzer (Eds.), Series, Inverse Problem, Image Analysis, and Medical
Imaging, 2002, 313, AMS, Providence, 97–116.
[19] M. A. El-Gebeily and I. T. Abbu-Zaid, On a finite difference method for singular
two-point boundary value problem, IMA J. Numer. Anal., 18:179–190, 1998.
[20] U. Flesch, The distribution of heat sources in the human head: a theoretical
consideration, J. Theor. Biol., 54:285–287, 1975.
[21] J. B. Garner and R. Shivaji, Diffusion problems with mixed nonlinear boundary
condition, J. Math. Anal. Appl., 148:422–430, 1990.
[22] J. Goh, A. Majid and A. I. Ismail, A quartic B-spline for second-order singular
boundary value problems, Comput. Math. Appl., 64:115–120, 1983.
[23] P. Hiltmann and P. Lory, On oxygen diffusion in a spherical cell with michaelismenten
oxygen uptake kinetics, Bull. Math. Biol., 45:661–664, 1983.
[24] R. K. Jain and P. Jain, Finite difference methods for a class of singular two-point
boundary value problems, Int. J. Comput. Math., 27:113–120, 1989.
[25] M. K. Kadalbajoo and K. S. Raman, Numerical solution of singular boundary
value problems by invariant imbedding, J. Comput. Phys., 55:268–277, 1984.
[26] M. K. Kadalbajoo and V. K. Aggarwal, Numerical solution of singular boundary
value problems via Chebyshev polynomial and B-spline, Appl. Math. Comput.,
160:851–863, 2005.
[27] M. K. Kadalbajoo and V. K. Aggarwal, B-spline method for a class of singular
two-point boundary value problems using optimal grid, Appl. Math. Comput.,
188:1856–1869, 2007.
[28] H. B. Keller, Numerical Methods for Two-Point Boundary Value Problems, Blaisdell
Publishing Co., Waltham Massachusetts, 1968.
[29] S. A. Khuri and A. Sayfy, A Twofold spline Chebychev linearization approach
for a class of singular second-order nonlinear differential equation, Results Math.,
63:817–835, 2013.
[30] M. Kumar, A three-point finite difference method for a class of singular two-point
boundary value problems, J. Comput. Appl. Math., 145:89–97, 2002.
[31] H. S. Lin, Oxygen diffusion in a spherical cell with nonlinear oxygen uptake
kinetics, J. Theor. Biol., 60:449–457, 1976.
[32] D. L. S. McElwain, A re-examination of oxygen diffusion in a spherical cell with
michaelis-menten oxygen uptake kinetics, J. Theor. Biol., 71:255–263, 1978.
[33] R. K. Pandey and A. K. Singh, On the convergence of a finite difference method
for a class of singular boundary value problems arising in physiology, J. Comput.
Appl. Math., 166:553–564, 2004.
[34] P. M. Prenter, Spline and Variational Methods, John Wiley & Sons, New York, 1975.
[35] J. Rashidinia, R. Mohammadi and R. Jalilian, The numerical solution of nonlinear
singular boundary value problems arising in physiology, Appl. Math. Comput.,
185:360–367, 2007.
[36] A. S. V. Ravi Kanth and Y. N. Reddy, A numerical method for singular two-point
boundary value problems via Chebyshev economization, Appl. Math. Comput.,
146:691–700, 2003.
[37] A. S. V. Ravi Kanth and Y. N. Reddy, Higher order finite difference method for
a class of singular boundary value problems, Appl. Math. Comput., 55:249–258, 2004.
[38] A. S. V. Ravi Kanth and Y. N. Reddy, Cubic spline for a class of singular twopoint
boundary value problems, Appl. Math. Comput., 170:733–740, 2005.
[39] A. S. V. Ravi Kanth and V. Bhattacharya, Cubic spline polynomial for a class
of non-linear singular two-point boundary value problems arising in physiology,
Appl. Math Comput., 174:768–774, 2006.
[40] G. W. Reddien, On the collocation method for singular two point boundary value
problems, Numer. Math., 25:427–432, 1975.
[41] R. D. Russell and L. F. Shampine, Numerical methods for singular boundary
value problems, SIAM J. Numel. Anal., 12:13–36, 1975.
[42] A. Sayfy and S. Khuri, A generalized algorithm for the order verification of
numerical methods, Far East J. Appl. Math., 33:295–306, 2008.
[43] I. J. Schoenberg, On Spline Functions. MRC Report 625, University of Wisconsin (1966).
[44] S. Taliaferro, A nonlinear singular boundary value problem, Nonlinear Anal.,
3:897–904, 1979.
[45] W. Wang, M. Cui and B. Han, A new method for solving a class of singular
two-point boundary value problems, Appl. Math. Comput., 206:721–727, 2008.
[46] Y. Wang, M. Tadi and M. Radenkovic, A numerical method for singular and singularly
perturbed Dirichlet-type boundary-value problems, Int. J. Appl. Math.
Research., 3:292–300, 2014.
[47] X. Zhang, Modified cubic B-spline solution of singular two-point boundary value
problems, J. Inf. Comput. Sci., 11:3167–3176, 2014.