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A sixth-order numerical method for a strongly nonlinear singular boundary value problem governing electrohydrodynamic flow in a circular cylindrical conduit

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  • Roul, Pradip
  • Madduri, Harshita
  • Kassner, Klaus

Abstract

This paper is concerned with the nonlinear singular boundary value problems for the electrohydrodynamic flow of a fluid in an ion drag configuration in a circular cylindrical conduit. The nonlinearity confronted in this problem is in the form of rational function. We develop a sixth-order numerical method based on sextic B-spline basis functions to obtain a more accurate result for such problem. The velocity field emerging in the electrohydrodynamic flow is computed. Further, the effects of the strength of nonlinearity and the Hartmann electric number on the velocity field are studied. The computational results reveal that nondimensional velocity at the centre line of the conduit increases with increasing Hartmann electric number and decreases with the increasing strength of nonlinearity. Error analysis of the sextic B-spline interpolation is supplemented.

Suggested Citation

  • Roul, Pradip & Madduri, Harshita & Kassner, Klaus, 2019. "A sixth-order numerical method for a strongly nonlinear singular boundary value problem governing electrohydrodynamic flow in a circular cylindrical conduit," Applied Mathematics and Computation, Elsevier, vol. 350(C), pages 416-433.
    • Handle: RePEc:eee:apmaco:v:350:y:2019:i:c:p:416-433
    DOI: 10.1016/j.amc.2018.12.070
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. S. C. S. Rao & M. Kumar, 2007. "B-Spline Collocation Method for Nonlinear Singularly-Perturbed Two-Point Boundary-Value Problems," Journal of Optimization Theory and Applications, Springer, vol. 134(1), pages 91-105, July.
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    Cited by:

    1. Naveed Ahmad Khan & Muhammad Sulaiman & Carlos Andrés Tavera Romero & Fawaz Khaled Alarfaj, 2021. "Numerical Analysis of Electrohydrodynamic Flow in a Circular Cylindrical Conduit by Using Neuro Evolutionary Technique," Energies, MDPI, vol. 14(22), pages 1-19, November.
    2. 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).
    3. Roul, Pradip & Prasad Goura, V.M.K., 2020. "A high order numerical method and its convergence for time-fractional fourth order partial differential equations," Applied Mathematics and Computation, Elsevier, vol. 366(C).
    4. 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.

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