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Applications of Quintic Hermite collocation with time discretization to singularly perturbed problems

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  • Arora, Shelly
  • Kaur, Inderpreet

Abstract

Singular perturbation problems have been discussed using collocation technique with quintic Hermite interpolating polynomials as base functions. These polynomials have the property to interpolate the function as well as its tangent at node points. To discretize the problem in temporal direction forward difference operator has been applied. The given technique is a combination of collocation and difference scheme. Parameter uniform convergence has been studied using the method given by Farrell and Hegarty (1991). Rate of convergence of quintic Hermite difference scheme has been found to depend upon node points. Applicability and computational effect of the scheme has been examined through numerical examples. Results have been presented graphically through surface plots as well as in tabular form.

Suggested Citation

  • Arora, Shelly & Kaur, Inderpreet, 2018. "Applications of Quintic Hermite collocation with time discretization to singularly perturbed problems," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 409-421.
    • Handle: RePEc:eee:apmaco:v:316:y:2018:i:c:p:409-421
    DOI: 10.1016/j.amc.2017.08.040
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    References listed on IDEAS

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    1. Dyksen, Wayne R. & Lynch, Robert E., 2000. "A new decoupling technique for the Hermite cubic collocation equations arising from boundary value problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 54(4), pages 359-372.
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    Cited by:

    1. Archna Kumari & Vijay K. Kukreja, 2023. "Survey of Hermite Interpolating Polynomials for the Solution of Differential Equations," Mathematics, MDPI, vol. 11(14), pages 1-28, July.
    2. Marasi, H.R. & Derakhshan, M.H., 2023. "Numerical simulation of time variable fractional order mobile–immobile advection–dispersion model based on an efficient hybrid numerical method with stability and convergence analysis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 368-389.

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    1. Marasi, H.R. & Derakhshan, M.H., 2023. "Numerical simulation of time variable fractional order mobile–immobile advection–dispersion model based on an efficient hybrid numerical method with stability and convergence analysis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 368-389.

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