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A compact finite difference method for a general class of nonlinear singular boundary value problems with Neumann and Robin boundary conditions

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  • Roul, Pradip
  • Prasad Goura, V.M.K.
  • Agarwal, Ravi

Abstract

In this paper, we develop and analyze a high order compact finite difference method (CFDM) for solving a general class of two-point nonlinear singular boundary value problems with Neumann and Robin boundary conditions arising in various physical models. Convergence result of this method is established through matrix analysis approach. To illustrate the applicability and accuracy of the method, we consider nine numerical examples, including heat conduction in the human head, equilibrium of isothermal gas sphere, oxygen-diffusion in a spherical cell and reaction–diffusion process in a spherical permeable catalyst. It is shown that the computational order of convergence of the proposed CFDM is four. The obtained results are compared with those obtained by other existing numerical methods.

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  • Roul, Pradip & Prasad Goura, V.M.K. & Agarwal, Ravi, 2019. "A compact finite difference method for a general class of nonlinear singular boundary value problems with Neumann and Robin boundary conditions," Applied Mathematics and Computation, Elsevier, vol. 350(C), pages 283-304.
    • Handle: RePEc:eee:apmaco:v:350:y:2019:i:c:p:283-304
    DOI: 10.1016/j.amc.2019.01.001
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    References listed on IDEAS

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    1. Roul, Pradip & Madduri, Harshita, 2019. "A new approximate method and its convergence for a strongly nonlinear problem governing electrohydrodynamic flow of a fluid in a circular cylindrical conduit," Applied Mathematics and Computation, Elsevier, vol. 341(C), pages 335-347.
    2. Goura, V.M.K. Prasad & Roul, Pradip, 2019. "Erratum to: B-spline collocation methods and their convergence for a class of nonlinear derivative dependent singular boundary value problems," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 198-201.
    3. Ren, Lei & Wang, Yuan-Ming, 2017. "A fourth-order extrapolated compact difference method for time-fractional convection-reaction-diffusion equations with spatially variable coefficients," Applied Mathematics and Computation, Elsevier, vol. 312(C), pages 1-22.
    4. Roul, Pradip & Prasad Goura, V.M.K., 2019. "B-spline collocation methods and their convergence for a class of nonlinear derivative dependent singular boundary value problems," Applied Mathematics and Computation, Elsevier, vol. 341(C), pages 428-450.
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    Cited by:

    1. Roul, Pradip & Prasad Goura, V.M.K., 2022. "A superconvergent B-spline technique for second order nonlinear boundary value problems," Applied Mathematics and Computation, Elsevier, vol. 414(C).
    2. Amit K. Verma & Biswajit Pandit & Lajja Verma & Ravi P. Agarwal, 2020. "A Review on a Class of Second Order Nonlinear Singular BVPs," Mathematics, MDPI, vol. 8(7), pages 1-50, June.
    3. Ramos, Higinio & Rufai, Mufutau Ajani, 2022. "An adaptive pair of one-step hybrid block Nyström methods for singular initial-value problems of Lane–Emden–Fowler type," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 497-508.

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