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Asymptotic numerical method for third-order singularly perturbed convection diffusion delay differential equations

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Abstract

In this paper, an asymptotic numerical method based on a fitted finite difference scheme and the fourth-order Runge–Kutta method with piecewise cubic Hermite interpolation on Shishkin mesh is suggested to solve singularly perturbed boundary value problems for third-order ordinary differential equations of convection diffusion type with a delay. An error estimate is derived using the supremum norm and it is of almost first-order convergence. A nonlinear problem is also solved using the Newton’s quasi linearization technique and the present asymptotic numerical method. Numerical results are provided to illustrate the theoretical results.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur, Chennai, Tamilnadu, 603 203, India

    V. Subburayan & R. Mahendran

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  1. V. Subburayan
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  2. R. Mahendran
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Correspondence to V. Subburayan.

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Communicated by Corina Giurgea.

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Subburayan, V., Mahendran, R. Asymptotic numerical method for third-order singularly perturbed convection diffusion delay differential equations. Comp. Appl. Math. 39, 194 (2020). https://doi.org/10.1007/s40314-020-01223-6

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  • DOI: https://doi.org/10.1007/s40314-020-01223-6

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