An efficient semi-numerical technique for solving nonlinear singular boundary value problems arising in various physical models

References

• G. Adomian, Solving Frontier Problems of Physics: The Decomposition Method, Kluwer Academic Publishers, Boston, 1994.
   Google Scholar
• G. Adomian and R. Rach, Inversion of nonlinear stochastic operators, J. Math. Anal. Appl. 91(1) (1983), pp. 39–46. doi: 10.1016/0022-247X(83)90090-2
   Web of Science ®Google Scholar
• T. Aziz and M. Kumar, A fourth-order finite-difference method based on non-uniform mesh for a class of singular two-point boundary value problems, J. Comput. Appl. Math. 136(1) (2001), pp. 337–342. doi: 10.1016/S0377-0427(00)00624-5
   Web of Science ®Google Scholar
• M.M. Chawla and C.P. Katti, Finite difference methods and their convergence for a class of singular two point boundary value problems, Numer. Math. 39(3) (1982), pp. 341–350. doi: 10.1007/BF01407867
   Web of Science ®Google Scholar
• M. Danish, S. Kumar, and S. Kumar, A note on the solution of singular boundary value problems arising in engineering and applied sciences: Use of OHAM, Comput. Chem. Eng. 36 (2012), pp. 57–67. doi: 10.1016/j.compchemeng.2011.08.008
   Web of Science ®Google Scholar
• J.-S. Duan, An efficient algorithm for the multivariable Adomian polynomials, Appl. Math. Comput. 217(6) (2010), pp. 2456–2467. doi: 10.1016/j.amc.2010.07.046
   Web of Science ®Google Scholar
• J.-S. Duan, New recurrence algorithms for the nonclassic Adomian polynomials, Comput. Math. Appl. 62(8) (2011), pp. 2961–2977. doi: 10.1016/j.camwa.2011.07.074
   Web of Science ®Google Scholar
• J.-S. Duan and R. Rach, A new modification of the Adomian decomposition method for solving boundary value problems for higher order nonlinear differential equations, Appl. Math. Comput. 218(8) (2011), pp. 4090–4118. doi: 10.1016/j.amc.2011.09.037
   Web of Science ®Google Scholar
• J.-S. Duan, R. Rach, A.M. Wazwaz, T. Chaolu, and Z. Wang, A new modified Adomian decomposition method and its multistage form for solving nonlinear boundary value problems with Robin boundary conditions, Appl. Math. Model. 37(2021) (2013), pp. 8687–8708. doi: 10.1016/j.apm.2013.02.002
   Web of Science ®Google Scholar
• R.C. Duggan and A.M. Goodman, Pointwise bounds for a nonlinear heat conduction model of the human head, Bull. Math. Biol. 48(2) (1986), pp. 229–236. doi: 10.1007/BF02460025
   PubMed Web of Science ®Google Scholar
• A. Ebaid, A new analytical and numerical treatment for singular two-point boundary value problems via the Adomian decomposition method, J. Comput. Appl. Math. 235(8) (2011), pp. 1914–1924. doi: 10.1016/j.cam.2010.09.007
   Web of Science ®Google Scholar
• I.L. El-Kalla, Error estimates for series solutions to a class of nonlinear integral equations of mixed type, J. Appl. Math. Comput. 38(1) (2012), pp. 341–351. doi: 10.1007/s12190-011-0482-3
   Google Scholar
• B.F. Gray, The distribution of heat sources in the human head-theoretical considerations, J. Theoret. Biol. 82(3) (1980), pp. 473–476. doi: 10.1016/0022-5193(80)90250-7
   PubMed Web of Science ®Google Scholar
• M. Inc and D.J. Evans, The decomposition method for solving of a class of singular two-point boundary value problems, Int. J. Comput. Math. 80(7) (2003), pp. 869–882. doi: 10.1080/0020716031000087087
   Web of Science ®Google Scholar
• 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(3) (2010), pp. 626–636. doi: 10.1016/j.mcm.2010.04.009
   Web of Science ®Google Scholar
• M. Kumar and N. Singh, Modified Adomian decomposition method and computer implementation for solving singular boundary value problems arising in various physical problems, Comput. Chem. Eng. 34(11) (2010), pp. 1750–1760. doi: 10.1016/j.compchemeng.2010.02.035
   Web of Science ®Google Scholar
• S.H. Lin, Oxygen diffusion in a spherical cell with nonlinear oxygen uptake kinetics, J. Theoret. Biol. 60(2) (1976), pp. 449–457. doi: 10.1016/0022-5193(76)90071-0
   PubMed Web of Science ®Google Scholar
• R. Rach, A convenient computational form for the Adomian polynomials, J. Math. Anal. Appl. 102(2) (1984), pp. 415–419. doi: 10.1016/0022-247X(84)90181-1
   Web of Science ®Google Scholar
• R.C. Rach, A new definition of the Adomian polynomials, Kybernetes 37(7) (2008), pp. 910–955. doi: 10.1108/03684920810884342
   Web of Science ®Google Scholar
• I. Rachuunkova, O. Koch, G. Pulverer, and E. Weinmuller, On a singular boundary value problem arising in the theory of shallow membrane caps, J. Math. Anal. Appl. 332(1) (2007), pp. 523–541. doi: 10.1016/j.jmaa.2006.10.006
   Web of Science ®Google Scholar
• A.S.V. Ravi Kanth and K. Aruna, He's variational iteration method for treating nonlinear singular boundary value problems, Comput. Math. Appl. 60(3) (2010), pp. 821–829. doi: 10.1016/j.camwa.2010.05.029
   Web of Science ®Google Scholar
• A.S.V. Ravi Kanth and Y.N. Reddy, Cubic spline for a class of singular two-point boundary value problems, Appl. Math. Comput. 170(2) (2005), pp. 733–740. doi: 10.1016/j.amc.2004.12.049
   Web of Science ®Google Scholar
• R. Singh and J. Kumar, An efficient numerical technique for the solution of nonlinear singular boundary value problems, Comput. Phys. Commun. 185(4) (2014), pp. 1282–1289. doi: 10.1016/j.cpc.2014.01.002
   Web of Science ®Google Scholar
• A.-M. Wazwaz, Approximate solutions to boundary value problems of higher order by the modified decomposition method, Comput. Math. Appl. 40(6–7) (2000), pp. 679–691. doi: 10.1016/S0898-1221(00)00187-5
   Web of Science ®Google Scholar
• A.-M. Wazwaz, The variational iteration method for solving nonlinear singular boundary value problems arising in various physical models, Commun. Nonlinear Sci. Numer. Simul. 16(10) (2011), pp. 3881–3886. doi: 10.1016/j.cnsns.2011.02.026
   Web of Science ®Google Scholar