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Chelyshkov collocation method for a class of mixed functional integro-differential equations

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  • Oğuz, Cem
  • Sezer, Mehmet

Abstract

In this study, a numerical matrix method based on Chelyshkov polynomials is presented to solve the linear functional integro-differential equations with variable coefficients under the initial-boundary conditions. This method transforms the functional equation to a matrix equation by means of collocation points. Also, using the residual function and Mean Value Theorem, an error analysis technique is developed. Some numerical examples are performed to illustrate the accuracy and applicability of the method.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:259:y:2015:i:c:p:943-954
    DOI: 10.1016/j.amc.2015.03.024
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    References listed on IDEAS

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    1. Dehghan, Mehdi & Shakourifar, Mohammad & Hamidi, Asgar, 2009. "The solution of linear and nonlinear systems of Volterra functional equations using Adomian–Pade technique," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2509-2521.
    2. M.K. Kadalbajoo & K.K. Sharma, 2002. "Numerical Analysis of Boundary-Value Problems for Singularly-Perturbed Differential-Difference Equations with Small Shifts of Mixed Type," Journal of Optimization Theory and Applications, Springer, vol. 115(1), pages 145-163, October.
    3. Javidi, M. & Golbabai, A., 2009. "Modified homotopy perturbation method for solving non-linear Fredholm integral equations," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1408-1412.
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    Cited by:

    1. 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.
    2. Hamid, Muhammad & Usman, Muhammad & Haq, Rizwan Ul & Tian, Zhenfu, 2021. "A spectral approach to analyze the nonlinear oscillatory fractional-order differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    3. Naserizadeh, L. & Hadizadeh, M. & Amiraslani, A., 2021. "Cubature rules based on a bivariate degree-graded alternative orthogonal basis and their applications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 231-245.
    4. Balcı, Mehmet Ali & Sezer, Mehmet, 2016. "Hybrid Euler–Taylor matrix method for solving of generalized linear Fredholm integro-differential difference equations," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 33-41.
    5. Rahimkhani, P. & Ordokhani, Y., 2022. "Chelyshkov least squares support vector regression for nonlinear stochastic differential equations by variable fractional Brownian motion," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    6. Çayan, Seda & Özhan, B. Burak & Sezer, Mehmet, 2022. "A Taylor-Splitting Collocation approach and applications to linear and nonlinear engineering models," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    7. Nikooeinejad, Z. & Heydari, M. & Loghmani, G.B., 2022. "A numerical iterative method for solving two-point BVPs in infinite-horizon nonzero-sum differential games: Economic applications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 200(C), pages 404-427.

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