A non-classical sinc-collocation method for the solution of singular boundary value problems arising in physiology

References

• M. Abdelhakem and Y.H. Youssri, Two spectral legendres derivative algorithms for Lane-Emden, Bratu equations, and singular perturbed problems, Appl. Numer. Math. 169 (2021), pp. 243–255.
   Web of Science ®Google Scholar
• J.A. Adam, A simplified mathematical model of tumor growth, Math. Biosci. 81 (1986), pp. 229–244.
   Web of Science ®Google Scholar
• A. Alipanah, Nonclassical pseudospectral method for a class of singular boundary value problems arising in physiology, Appl. Math. 2(2) (2012), pp. 1–4.
   Google Scholar
• A.G. Atta, G.M. Moatimid, and Y.H. Youssri, Generalized Fibonacci operational collocation approach for fractional initial value problems, Int. J. Appl. Comput. Math 5 (2019), pp. 1–11. doi:10.1007/s40819-018-0597-4
   Google Scholar
• E. Babolian, A. Eftekhari, and A. Saadatmandi, A Sinc-Galerkin technique for the numerical solution of a class of singular boundary value problems, Comp. Appl. Math. 34(1) (2013), pp. 45–63. doi:10.1007/s4034-013-0103-x
   Google Scholar
• B. Bialecki, Sinc-collocation methods for two-point boundary value problems, IMA J. Numer. Anal. 11 (1991), pp. 357–375.
   Web of Science ®Google Scholar
• H. Caglar, N. Caglar, and M. ozer, B-spline solution of nonlinear singular boundary value problems arising in physiology, Chaos Solit Fractals 39 (2009), pp. 1232–1237.
   Web of Science ®Google Scholar
• M. Dehghan and A. Saadatmandi, The numerical solution of a nonlinear system of second-order boundary value problems using the Sinc-collocation method, Math. Comput. Model 46 (2007), pp. 1434–1441.
   Web of Science ®Google Scholar
• M. El-Gamel, S.H. Behiry, and H. Hashish, Numerical method for the solution of special nonlinear fourth–order boundary value problems, Appl. Math. Comput. 145 (2003), pp. 717–734.
   Web of Science ®Google Scholar
• B.F. Gray, The distribution of heat sources in the human head: a theoretical consideration, J. Theor. Biol. 82 (1980), pp. 473–476.
   PubMed Web of Science ®Google Scholar
• H.P. Greenpan, Models for the growth of solid tumor as a problem by diffusion, Appl. Math. Comput. 30 (1972), pp. 215–222.
   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 (2010), pp. 626–636.
   Web of Science ®Google Scholar
• S.A. Khoury and A. Sayfy, A mixed decomposition-spline approach for the numerical solution of a class of singular boundary value problems, Appl. Math. Model. 40(7-8) (2016), pp. 4664–4680.
   Web of Science ®Google Scholar
• J. Lund and K. Bowers, Sinc Methods for Quadrature and Differential Equations, SIAM, Philadelphia, PA, 1992.
   Google Scholar
• D.L.S. Mcelwain, A re-examination of Oxygen diffusion in a spherical cell with Michaelis Menten oxygen uptake kinetics, J. Theor. Biol. 71 (1978), pp. 255–263.
   PubMed Web of Science ®Google Scholar
• A.C. Morlet, Convergence of the sinc method for a fourth-order ordinary differential equation with an application, SIAM J. Numer. Anal. 32 (1995), pp. 1475–1503.
   Web of Science ®Google Scholar
• S. Narasimhan, J. Majdalani, and F. Stenger, A first step in applying the sinc collocation method to the nonlinear Navier-Stokes, Numer. Heat Transfer B 41 (2002), pp. 447–462.
   Web of Science ®Google Scholar
• M. Nosrati and E. Hashemizadeh, Wavelet Galerkin method for solving of a class of singular boundary value problems arising in physiology, Appl. Math. Comput. 250 (2015), pp. 260–269.
   Web of Science ®Google Scholar
• T. Okayama, T. Matsuo, and M. Sugihara, Sinc-collocation methods for weakly singular Fredholm integral equations of the second kind, J. Comput. Appl. Math. 234 (2010), pp. 1211–1227.
   Web of Science ®Google Scholar
• R.K. Pandey, A note on a finite difference method for a class of singular boundary-value problems in physiology, Int. J. Comput. Math. 74 (2000), pp. 127–132.
   Web of Science ®Google Scholar
• K. Parand, M. Dehghanb, and A. Pirkhedri, The Sinc-collocation method for solving the Thomas–Fermi equation, J. Comput. Appl. Math. 237 (2013), pp. 244–252.
   Web of Science ®Google Scholar
• K. Parand and A. Pirkhedri, Sinc-collocation method for solving astrophysics equations, New Astron 15 (2010), pp. 533–537.
   Web of Science ®Google Scholar
• A.S.V. R. Kanth and V. Bhattacharya, Cubic spline for a class of non-linear singular boundary value problems arising in physiology, Appl. Math. Comput. 174 (2006), pp. 768–774.
   Web of Science ®Google Scholar
• R. Rach, A.-M. Wazwaz, and J.-S. Duan, A reliable analysis of Oxygen diffusion in a spherical cell with nonlinear oxygen uptake kinetics, Int. J. Biomath. 7 (2014), p. 1450020.
   Web of Science ®Google Scholar
• J. Rashidinia and A. Barati, Numerical solutions of one-dimensional non-linear parabolic equations using Sinc collocation method, Ain Shams Eng. J. 6 (2015), pp. 381–389.
   Web of Science ®Google Scholar
• J. Rashidinia, R. Mohamamdi, and R. Jalilian, The numerical solution of nonlinear singular boundary value problems arising in physiology, Appl. Math. Comput. 185 (2007), pp. 360–367.
   Web of Science ®Google Scholar
• J. Rashidinia and M. Zarebnia, Solution of a Volterra integral equation by the Sinc-collocation method, J. Comput. Appl. Math. 206 (2007), pp. 801–813.
   Web of Science ®Google Scholar
• A. Saadatmandi, M. Razzaghi, and M. Dehghan, Sinc-collocation methods for the solution of Hallen's integral equation, J. Electromag. Waves Appl. 19(2) (2005), pp. 245–256.
   Web of Science ®Google Scholar
• M. Sababheh and A. Al-khaled, Some convergence results on Sinc interpolation, J. Inequal. Pure Appl. Math. 4 (2003), pp. 32–48.
   Google Scholar
• A. Shidfar, R. Zolfaghari, and J. Damirchi, Application of Sinc-collocation method for solving an inverse problem, J. Comput. Appl. Math 223 (2009), pp. 545–554.
   Web of Science ®Google Scholar
• B. Shizgal, A Gaussian quadrature procedure for use in the solution of the Boltzmann equation and related problems, J. Comput. Phys. 41 (1981), pp. 309–328.
   Web of Science ®Google Scholar
• B. Shizgal and H. Chen, The quadrature discretization method (QDM) in the solution of the Schrodinger equation with non-classical basis functions, J. Chem. Phys. 104(11) (1996), pp. 4137–4150.
   Web of Science ®Google Scholar
• R. Singh, J. Kumar, and G. Nelakanti, Approximate series solution of nonlinear singular boundary value problems arising in physiology, Sci. World J. 2014 (2014), p. 945872.
   Web of Science ®Google Scholar
• R. Singh, A.-M. Wazwaz, and J. Kumar, An efficient semi-numerical technique for solving nonlinear singular boundary value problems arising in various physical models, Int. J. Comput. Math. 93(8) (2016), pp. 1330–1346.
   Web of Science ®Google Scholar
• F. Stenger, Approximations via Whittakers cardinal function, J. Approx. Theory. 17 (1976), pp. 222–240.
   Web of Science ®Google Scholar
• F. Stenger, A Sinc-Galerkin method of solution of boundary value problems, Math. Comput. 33 (1979), pp. 85–109.
   Web of Science ®Google Scholar
• F. Stenger, Numerical Methods Based on Sinc and Analytic Functions, Springer, NewYork, 1993.
   Google Scholar
• F. Stenger, Sincpack-Summary of Basic Sinc Methods, Department of Computer Science, University of Utah, Salt Lake City, UT, 1995.
   Google Scholar
• K. Thula and P. Roul, A high-order B-Spline collocation method for solving nonlinear singular boundary value problems arising in engineering and applied science, Mediterr. J. Math. 15 (2018), p. 176. doi:10.1007/s0009-018-1220-y
   Web of Science ®Google Scholar
• D.F. Winter, K. Bowers, and J. Lund, Wind-driven currents in a sea with a variable Eddy viscosity calculated via a Sinc–Galerkin technique, Int. J. Numer. Methods Fluids 33 (2000), pp. 1041–1073.
   Web of Science ®Google Scholar
• Y.H. Youssri, W.M. Abd-Elhameed, and M. Abdelhakem, A robust spectral treatment of a class of initial value problems using modified Chebyshev polynomials, Math. Methods. Appl. Sci. 44(11) (2021), pp. 9224–9236. doi:10.1002/mma.7347
   Web of Science ®Google Scholar
• F. Zhou and X. Xu, Numerical solutions for the linear and nonlinear singular boundary value problems using Laguerre wavelets, Adv. Differ. Equ. 2016(1) (2016), pp. 1–15. doi:10.1186/s13662-016-0754-1.
   Web of Science ®Google Scholar