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A numerical approach with error estimation to solve general integro-differential–difference equations using Dickson polynomials

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  • Kürkçü, Ömür Kıvanç
  • Aslan, Ersin
  • Sezer, Mehmet

Abstract

In this paper, a matrix method based on the Dickson polynomials and collocation points is introduced for the numerical solution of linear integro-differential–difference equations with variable coefficients under the mixed conditions. In addition, in order to improve the numerical solution, an error analysis technique relating to residual functions is performed. Some linear and nonlinear numerical examples are given to illustrate the accuracy and applicability of the method. Eventually, the obtained results are discussed according to the parameter-α of Dickson polynomials and the residual error estimation.

Suggested Citation

  • Kürkçü, Ömür Kıvanç & Aslan, Ersin & Sezer, Mehmet, 2016. "A numerical approach with error estimation to solve general integro-differential–difference equations using Dickson polynomials," Applied Mathematics and Computation, Elsevier, vol. 276(C), pages 324-339.
    • Handle: RePEc:eee:apmaco:v:276:y:2016:i:c:p:324-339
    DOI: 10.1016/j.amc.2015.12.025
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    References listed on IDEAS

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    1. Oğuz, Cem & Sezer, Mehmet, 2015. "Chelyshkov collocation method for a class of mixed functional integro-differential equations," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 943-954.
    2. Bellen, Alfredo & Zennaro, Marino, 2003. "Numerical Methods for Delay Differential Equations," OUP Catalogue, Oxford University Press, number 9780198506546.
    3. Bülbül, Berna & Sezer, Mehmet, 2015. "A numerical approach for solving generalized Abel-type nonlinear differential equations," Applied Mathematics and Computation, Elsevier, vol. 262(C), pages 169-177.
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