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A new collocation approach for solving systems of high-order linear Volterra integro-differential equations with variable coefficients

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  • Mirzaee, Farshid
  • Hoseini, Seyede Fatemeh

Abstract

This paper contributes an efficient numerical approach for solving the systems of high-order linear Volterra integro-differential equations with variable coefficients under the mixed conditions. The method we have used consists of reducing the problem to a matrix equation which corresponds to a system of linear algebraic equations. The obtained matrix equation is based on the matrix forms of Fibonacci polynomials and their derivatives by means of collocations. In addition, the method is presented with error. Numerical results with comparisons are given to demonstrate the applicability, efficiency and accuracy of the proposed method. The results of the examples indicated that the method is simple and effective, and could provide an approximate solution with high accuracy or exact solution of the system of high-order linear Volterra integro-differential equations.

Suggested Citation

  • Mirzaee, Farshid & Hoseini, Seyede Fatemeh, 2017. "A new collocation approach for solving systems of high-order linear Volterra integro-differential equations with variable coefficients," Applied Mathematics and Computation, Elsevier, vol. 311(C), pages 272-282.
    • Handle: RePEc:eee:apmaco:v:311:y:2017:i:c:p:272-282
    DOI: 10.1016/j.amc.2017.05.031
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    References listed on IDEAS

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    1. Mirzaee, Farshid & Hoseini, Seyede Fatemeh, 2016. "Application of Fibonacci collocation method for solving Volterra–Fredholm integral equations," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 637-644.
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    Cited by:

    1. Zhao, Hengzhi & Zhang, Jiwei & Lu, Jing, 2023. "Numerical approximate controllability for unidimensional parabolic integro-differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 575-596.
    2. Bulai, I.M. & De Bonis, M.C. & Laurita, C. & Sagaria, V., 2023. "Modeling metastatic tumor evolution, numerical resolution and growth prediction," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 721-740.

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    2. Amiri, Sadegh & Hajipour, Mojtaba & Baleanu, Dumitru, 2020. "A spectral collocation method with piecewise trigonometric basis functions for nonlinear Volterra–Fredholm integral equations," Applied Mathematics and Computation, Elsevier, vol. 370(C).

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