### New Cubic B-spline Approximation for Solving Non-linear Singular Boundary Value Problems Arising in Physiology

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M. Abbas, A. Abd. Majid, A.I. Md. Ismail and A. Rashid, Numerical method using cubic Bspline for a strongly coupled reaction-diffusion system, PloS-One 9 (1) (2014), e83265, DOI: 10.1371/journal.pone.0083265.

M. Abbas, A. Abd. Majid, A.I. Md. Ismail and A. Rashid, The application of cubic trigonometric Bspline to the numerical solution of the hyperbolic problems, Applied Mathematics and Computation 239 (2014), 74 – 88, DOI: 10.1016/j.amc.2014.04.031.

M. Abukhaled, S.A. Khuri and A. Sayfy, A numerical approach for solving a class of singular boundary value problems arising in physiology, International Journal of Numerical Analysis and Modeling 8 (2) (2011), 353 – 363.

E.L. Albasiny and W.D. Hoskins, Cubic spline solutions to two-point boundary value problems, The Computer Journal 12 (2) (1969), 151 – 153, DOI: 10.1093/comjnl/12.2.151.

E. Babolian, A. Iftikhari and A. Saadatmandi, A Sinc-Galerkin technique for the numerical solution of a class of singular boundary value problems, Computational and Applied Mathematics 34 (1) (2015), 45 – 63, DOI: 10.1007/s40314-013-0103-x.

W.G. Bickley, Piecewise cubic interpolation and two point boundary-value problems, Computer Journal 11 (1968), 202 – 208, DOI: 10.1093/comjnl/11.2.206.

C.D. Boor, A Practical Guide to Splines, Springer-Verlag, New York (1978).

N. Caglar and H. Caglar, B-spline solution of singular boundary value problems, Applied Mathematics and Computation 182 (2) (2006), 1509 – 1513, DOI: 10.1016/j.amc.2006.05.035.

H. Caglar, N. Caglar and M. Ozer, B-spline solution of non-linear singular boundary value problems arising in physiology, Chaos, Solitons & Fractals 39 (3) (2009), 1232 – 1237, DOI: 10.1016/j.chaos.2007.06.007.

Z. Cen, Numerical study for a class of singular two-point boundary value problems using Green’s functions, Applied Mathematics and Computation 183 (1) (2006), 10 – 16, DOI: 10.1016/j.amc.2006.01.096.

M.M. Chawala, R. Subramanian and H.L. Sathi, A fourth order method for a singular twopoint boundary value problem, BIT Numerical Mathematics 28 (1) (1988), 88 – 97, DOI: 10.1007/BF01934697.

U. Flesch, The distribution of heat sources in the human head: a theoretical consideration, Journal of Theoretical Biology 54 (2) (1975), 285 – 287, DOI: 10.1016/S0022-5193(75)80131-7.

D.J. Fyfe, The use of cubic splines in the solution of two-point boundary value problems, The Computer Journal 12 (2) (1969), 188 – 192, DOI: 10.1093/comjnl/12.2.188.

J.B. Garner and R. Shivaji, Diffusion problems with a mixed nonlinear boundary condition, Journal of Mathematical Analysis and Applications 148 (2) (1990), 422 – 430, DOI: 10.1016/0022-247X(90)90010-D.

J. Goh, A. Abd. Majid and A.I. Md. Ismail, A quartic B-spline for second-order singular boundary value problems, Computers & Mathematics with Applications 64 (2) (2012), 115 – 120, DOI: 10.1016/j.camwa.2012.01.022.

J. Goh, A. Abd. Majid and A.I. Md. Ismail, Extended cubic uniform B-spline for a class of singular boundary value problems, Nuclear Physics 2 (2011), 4 pages.

A.S.V.R. Kanth and K. Aruna, He’s variational iteration method for treating nonlinear singular boundary value problems, Computers & Mathematics with Applications 60 (3) (2010), 821 – 829, DOI: 10.1016/j.camwa.2010.05.029.

S.A. Khuri and A. Sayfy, A novel approach for the solution of a class of singular boundary value problems arising in physiology, Mathematical and Computer Modelling 52 (3) (2010), 626 – 636, DOI: 10.1016/j.mcm.2010.04.009.

F.G. Lang and X.P. Xu, A new cubic B-spline method for approximating the solution of a class of nonlinear second-order boundary value problem with two dependent variables, ScienceAsia 40 (6) (2014), 444 – 450, DOI: 10.2306/scienceasia1513-1874.2014.40.444.

S.H. Lin, Oxygen diffusion in a spherical cell with nonlinear oxygen uptake kinetics, Journal of Theoretical Biology 60 (2) (1976), 449 – 457, DOI: 10.1016/0022-5193(76)90071-0.

D.L.S. McElwain, A re-examination of oxygen diffusion in a spherical cell with Michaelis-Menten oxygen uptake kinetics, Journal of Theoretical Biology 71 (2) (1978), 255 – 263, DOI: 10.1016/0022-5193(78)90270-9.

M. Mohsenyzadeh, K. Maleknejad and R. Ezzati, A numerical approach for the solution of a class of singular boundary value problems arising in physiology, Advances in Difference Equations 2015 (1) (2015), 231, DOI: 10.1186/s13662-015-0572-x.

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, Journal of Computational and Applied Mathematics 166 (2) (2004), 553 – 564, DOI: 10.1016/j.cam.2003.09.053.

K. Parand, M. Dehghan, A.R. Rezaei and S.M. Ghaderi, An approximation algorithm for the solution of the nonlinear Lane–Emden type equations arising in astrophysics using Hermite functions collocation method, Computer Physics Communications 181 (6) (2010), 1096 – 1108, DOI: 10.1016/j.cpc.2010.02.018.

J. Rashidinia, R. Mohammadi and R. Jalilian, The numerical solution of non-linear singular boundary value problems arising in physiology, Applied Mathematics and Computation 185 (1) (2007), 360 – 367, DOI: 10.1016/j.amc.2006.06.104.

P. Rentrop, A Taylor series method for the numerical solution of two-point boundary value problems, Numerische Mathematik 31 (4) (1978), 359 – 375, DOI: 10.1007/BF01404566.

R.D. Russell and L.F. Shampine, Numerical methods for singular boundary value problems, SIAM Journal on Numerical Analysis 12 (1) (1975), 13 – 36, DOI: 10.1137/0712002.

R. Singh and J. Kumar, An efficient numerical technique for the solution of nonlinear singular boundary value problems, Computer Physics Communications 185 (4) (2014), 1282 – 1289, DOI: 10.1016/j.cpc.2014.01.002.

R. Singh, Abd. M. Wazwaz and J. Kumar, An efficient semi-numerical technique for solving nonlinear singular boundary value problems arising in various physical models, International Journal of Computer Mathematics 93 (8) (2016), 1330 – 1346, DOI: 10.1080/00207160.2015.1045888.

Y. Wang, H. Yu, F. Tan and S. Li, Using an effective numerical method for solving a class of Lane-Emden equations, Abstract and Applied Analysis, 2004 (2004), Article ID 735831, 8 pages, DOI: 10.1155/2014/735831.

Abd. M. Wazwaz, The variational iteration method for solving nonlinear singular boundary value problems arising in various physical models, Communications in Nonlinear Science and Numerical Simulation 16 (10) (2011), 3881 – 3886, DOI: 10.1016/j.cnsns.2011.02.026.

L.J. Xie, C.L. Zhou and S. Xu, An effective numerical method to solve a class of nonlinear singular boundary value problems using improved differential transform method, SpringerPlus 5 (1) (2016), 1066, DOI: 10.1186/s40064-016-2753-9.

DOI: http://dx.doi.org/10.26713%2Fcma.v9i3.802

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