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Fitted Numerical Method with Linear Interpolation for Third-Order Singularly Perturbed Delay Problems

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Differential Equations and Applications (ICABS 2019)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 368))

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Abstract

Singularly perturbed third-order ordinary delay differential equation with a discontinuous source term and discontinuous convection coefficient is considered in this article. To obtain a numerical approximate solution, a layer adapted mesh called the Shishkin mesh is constructed. On this mesh, a fitted finite difference method with piecewise linear interpolation is applied. Also, we present some classes of nonlinear problems. An error estimate is derived and is found to be of almost first-order convergence. Numerical results are given to validate the theoretical results

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Author information

Authors and Affiliations

  1. Department of Mathematics, Faculty of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur, 603203, TN, India

    R. Mahendran & V. Subburayan

Authors
  1. R. Mahendran
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  2. V. Subburayan
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Bishop Heber College, Tiruchirappalli, Tamil Nadu, India

    Valarmathi Sigamani

  2. Institute for Numerical Computation and Analysis, Dublin, Ireland

    John J. H. Miller

  3. National Institute of Technology, Tiruchirappalli, Tamil Nadu, India

    Shivaranjani Nagarajan

  4. Bishop Heber College, Tiruchirappalli, Tamil Nadu, India

    Parthiban Saminathan

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Mahendran, R., Subburayan, V. (2021). Fitted Numerical Method with Linear Interpolation for Third-Order Singularly Perturbed Delay Problems. In: Sigamani, V., Miller, J.J.H., Nagarajan, S., Saminathan, P. (eds) Differential Equations and Applications. ICABS 2019. Springer Proceedings in Mathematics & Statistics, vol 368. Springer, Singapore. https://doi.org/10.1007/978-981-16-7546-1_6

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