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A matched Hermite-Taylor matrix method to solve the combined partial integro-differential equations having nonlinearity and delay terms

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Abstract

In this study, a matched numerical method based on Hermite and Taylor matrix-collocation techniques is developed to obtain the numerical solutions of a combination of the partial integro-differential equations (PIDEs) under Dirichlet boundary conditions, which involve the nonlinearity, delay and Volterra integral terms. These type equations govern wide variety applications in physical sense. The present method easily constitutes the matrix relations of the linear and nonlinear terms in a considered PIDE, using the eligibilities of the Hermite and Taylor polynomials. It thus directly produces a polynomial solution by eliminating a matrix system of nonlinear algebraic functions gathered from the matrix relations. Besides, the validity and precision of the method are tested on stiff examples by fulfilling several error computations. One can state that the method is fast, validate and productive according to the numerical and graphical results

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Acknowledgements

The authors would like to thank anonymous reviewers for their constructive and valuable comments, which led to the improvement of the paper.

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Authors and Affiliations

  1. Department of Mathematics, Manisa Celal Bayar University, Manisa, 45140, Turkey

    Elif Yalçın & Mehmet Sezer

  2. Department of Engineering Basic Sciences, Konya Technical University, Konya, 42250, Turkey

    Ömür Kıvanç Kürkçü

Authors
  1. Elif Yalçın
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  2. Ömür Kıvanç Kürkçü
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  3. Mehmet Sezer
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Correspondence to Ömür Kıvanç Kürkçü.

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Communicated by Hui Liang.

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Yalçın, E., Kürkçü, Ö.K. & Sezer, M. A matched Hermite-Taylor matrix method to solve the combined partial integro-differential equations having nonlinearity and delay terms. Comp. Appl. Math. 39, 280 (2020). https://doi.org/10.1007/s40314-020-01331-3

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  • DOI: https://doi.org/10.1007/s40314-020-01331-3

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