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Approximate Solutions for a Class of Nonlinear Fredholm and Volterra Integro-Differential Equations Using the Polynomial Least Squares Method

Author

Listed:
  • Bogdan Căruntu

    (Department of Mathematics, Politehnica University of Timişoara, 300006 Timişoara, Romania
    These authors contributed equally to this work.)

  • Mădălina Sofia Paşca

    (Department of Mathematics, Politehnica University of Timişoara, 300006 Timişoara, Romania
    Department of Mathematics, West University of Timişoara, 300223 Timişoara, Romania
    These authors contributed equally to this work.)

Abstract

We apply the polynomial least squares method to obtain approximate analytical solutions for a very general class of nonlinear Fredholm and Volterra integro-differential equations. The method is a relatively simple and straightforward one, but its precision for this type of equations is very high, a fact that is illustrated by the numerical examples presented. The comparison with previous approximations computed for the included test problems emphasizes the method’s simplicity and accuracy.

Suggested Citation

  • Bogdan Căruntu & Mădălina Sofia Paşca, 2021. "Approximate Solutions for a Class of Nonlinear Fredholm and Volterra Integro-Differential Equations Using the Polynomial Least Squares Method," Mathematics, MDPI, vol. 9(21), pages 1-13, October.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:21:p:2692-:d:662985
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    References listed on IDEAS

    as
    1. Ming, Wanyuan & Huang, Chengming, 2017. "Collocation methods for Volterra functional integral equations with non-vanishing delays," Applied Mathematics and Computation, Elsevier, vol. 296(C), pages 198-214.
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