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An efficient numerical algorithm for solving nonlinear Volterra integral equations in the reproducing kernel space

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Abstract

The main purpose of this paper is to approximate the solution of the nonlinear Volterra integral equation numerically in the reproducing kernel space. Consequently, in the study, combining Quasi-Newton’s method and the least-square method, we develop a new method for solving this kind of equation. This technique transforms the nonlinear Volterra integral equation into a linear algebraic system of equations, which can be solved by using the least-square method breezily. At the same time, to ensure the preciseness of the method, we strictly analyze the existence and uniqueness of \(\varepsilon \)-approximate solution and its convergence. Finally, we illustrate the accuracy and reliability of this method by giving some examples.

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Acknowledgements

This study was supported by National Natural Science Funds of China by Grant Number 12101164; Harbin Normal University Postgraduate Innovative Research Project by Grant Number HSDSSCX2022-40; Doctoral Foundation of Harbin Normal University by Grant number XKB202011.

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  1. Yanxin Xu contributed equally to this work.

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  1. Harbin Normal University, Harbin, 150025, Heilongjiang, China

    Xuefei Dai, Jing Niu & Yanxin Xu

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Dai, X., Niu, J. & Xu, Y. An efficient numerical algorithm for solving nonlinear Volterra integral equations in the reproducing kernel space. J. Appl. Math. Comput. 69, 3131–3149 (2023). https://doi.org/10.1007/s12190-023-01874-8

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