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Triangular functions for numerical solution of the nonlinear Volterra integral equations

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Abstract

In this paper, a new numerical iterative method based on the successive approximations method for solving nonlinear Hammerstein Volterra integral equations of the second kind is proposed. The main approximation tool is based on triangular functions. Also, the convergence analysis and numerical stability of the proposed method are proved. Finally, some numerical examples verify the theoretical results and show the accuracy of the method.

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Acknowledgements

The author is grateful to the anonymous referees and the editorial board for their careful reading and helpful suggestions on the improvement of the article.

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

    Manochehr Kazemi

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Kazemi, M. Triangular functions for numerical solution of the nonlinear Volterra integral equations. J. Appl. Math. Comput. 68, 1979–2002 (2022). https://doi.org/10.1007/s12190-021-01603-z

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