References
- 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 (2011), pp. 353–363.
- J.V. Baxley and S.B. Robinson, Nonlinear boundary value problems for shallow membrane caps. II, J. Comput. Appl. Math. 88 (1998), pp. 203–224.
- H. Caglar, N. Caglar, and M. Ozer, B-Spline solution of non-linear singular boundary value problems arising in physiology, Chaos Solitions Fractals. 39 (2009), pp. 1232–1237.
- P.L. Chambre, On the solution of the Poisson–Boltzmann equation with the application to the theory of thermal explosions, J. Chem. Phys. 20 (1952), pp. 1795–1797.
- C. De Boor, A Practical Guide to Splines, NewYork: Springer-Verlag, 1978.
- H.S. Fogler, Elements of Chemical Reaction Engineering, 2nd ed., Prentice-Hall Inc, New Jersey, 1992.
- B.F. Gray, The distribution of heat sources in the human head: A theoretical consideration, J. Theoret. Biol. 82 (1980), pp. 473–476.
- P. Henrici, Discrete Variable Methods in Ordinary Differential Equations, John Wiley and Sons, New York, NY, USA, 1962.
- W.D. Hoskins and D.S. Meek, Linear dependence relations for polynomial splines at midknots, BIT. 15 (1975), pp. 272–276.
- S.A. Khuri and A. Sayfy, A novel approach for the solution of a class of singular boundary value problems arising in physiology, Math. Comput. Model. 52 (2010), pp. 626–636.
- S.A. Khuri and A. Sayfy, A mixed decomposition-spline approach for the numerical solution of a class of singular boundary value problems, Appl. Math. Model. 40 (2016), pp. 4664–4680.
- H.S. Lin, Oxygen diffusion in a spherical cell with nonlinear oxygen uptake kinetics, J. Theor. Biol. 60 (1976), pp. 449–457.
- T.R. Lucas, Error bound for interpolating cubic spline under various end conditions, Siam. J. Numer. Anal. 11 (1974), pp. 569–584.
- A. Mastroberardino, Homotopy analysis method applied to electro-hydrodynamic flow, Commun. Nonlinear Sci. Numer. Simul. 16 (2011), pp. 2730–2736.
- P.M. Prenter, Splines and Variational Methods, John Wiley & Sons, New York, 1975.
- R. Qu and R.P. Agarwal, A collocation method for solving a class of singular nonlinear two-point boundary value problems, J. Comput. Appl. Math. 83 (1997), pp. 147–163.
- I. Rachunkov', G. Pulverer, and E. Weinmller, A unified approach to singular problems arising in the membrane theory, Appl. Math. 55 (2010), pp. 47–75.
- A.S.V. Ravi Kanth and K. Aruna, He's variational iteration method for treating nonlinear singular boundary value problem, Comput. Math. Appl. 60 (2010), pp. 821–829.
- P. Roul, Doubly singular boundary value problems with derivative dependent source function: A fast converging iterative approach, Math. Methods Appl. Sci. 42(1) (2021), pp. 354–374.
- P. Roul and D. Biswal, A new numerical approach for solving a class of singular two-point boundary value problems, Numer. Algorithms. 75 (2017), pp. 531–552.
- P. Roul, H. Madduri, and K. Kassner, A new iterative algorithm for a strongly nonlinear singular boundary value problem, J.Comput. Appl. Math. 351 (2019), pp. 167–178.
- P. Roul and V.M.K. Prasad Goura, B-spline collocation methods and their convergence for a class of nonlinear derivative dependent singular boundary value problems, Appl. Math. Comput. 341 (2019), pp. 428–450.
- P. Roul and U. Warbhe, A novel numerical approach and its convergence for numerical solution of nonlinear doubly singular boundary value problems, J. Comput. Appl. Math. 296 (2016), pp. 661–676.
- R. Singh and J. Kumar, The Adomian decomposition method with Green's function for solving nonlinear singular boundary value problems, J. Appl. Math. Comput. 44 (2014), pp. 397–416.
- U. Yucel and M. Sari, Differential quadrature method (DQM) for a class of singular two-point boundary value problem, Int. J. Comput. Math. 86 (2009), pp. 465–475.
- Y Zhu, Quartic-spline collocation methods for fourth-order two-point boundary value problems, Master's thesis, University of Toronto, 2001.