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Application of bivariate fuzzy Bernstein polynomials to solve two-dimensional fuzzy integral equations

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Abstract

Numerical solutions of two-dimensional fuzzy Fredholm integral equations of the second kind (2DFFIE2) via bivariate fuzzy Bernstein polynomials are proposed in this paper. We introduce a numerical iterative procedure using successive approximations method to approximate the solution of 2DFFIE2. We prove the convergence of the method and define the notion of numerical stability of the algorithm with respect to the choice of the first iteration. This numerical stability is proved and finally, some numerical experiments confirm the theoretical results and illustrate the efficiency and accuracy of the method.

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Acknowledgments

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

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Authors and Affiliations

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

    R. Ezzati & S. M. Sadatrasoul

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  1. R. Ezzati
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  2. S. M. Sadatrasoul
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Correspondence to R. Ezzati.

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Communicated by V. Loia.

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Ezzati, R., Sadatrasoul, S.M. Application of bivariate fuzzy Bernstein polynomials to solve two-dimensional fuzzy integral equations. Soft Comput 21, 3879–3889 (2017). https://doi.org/10.1007/s00500-016-2038-9

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  • DOI: https://doi.org/10.1007/s00500-016-2038-9

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