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Using Bernstein multi-scaling polynomials to obtain numerical solution of Volterra integral equations system

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Abstract

In this paper, first, Bernstein multi-scaling polynomials (BMSPs), which are generalization of Bernstein polynomials (BPs), are introduced and some of their properties are explained. Then, a new method based on BMSPs to achieved numerical solution for system of nonlinear integral equations is proposed. The proposed method converted the system of integral equations to a nonlinear system. To evaluate the efficiency of the proposed method, some systems of nonlinear integral equations are solved, and their numerical solutions are compared with other similar methods.

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Acknowledgements

The authors are grateful to anonymous referees, especially for their constructive comments and suggestions.

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Authors and Affiliations

  1. Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran

    A. R. Yaghoobnia & R. Ezzati

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  1. A. R. Yaghoobnia
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  2. R. Ezzati
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Correspondence to R. Ezzati.

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Communicated by Hui Liang.

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Yaghoobnia, A.R., Ezzati, R. Using Bernstein multi-scaling polynomials to obtain numerical solution of Volterra integral equations system. Comp. Appl. Math. 39, 170 (2020). https://doi.org/10.1007/s40314-020-01198-4

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  • DOI: https://doi.org/10.1007/s40314-020-01198-4

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