An innovative iterative approach to solving Volterra integral equations of second kind

Mohammed Abdulshareef Hussein; Hassan Kamil Jassim; Ali Kareem Jassim

doi:10.14311/AP.2024.64.0087

Authors

Mohammed Abdulshareef Hussein Al-Ayen University, Scientific Research Center, 64001 Nasiriyah, Iraq; Ministry of Education, Education Directorate of Thi-Qar, 64001 Nasiriyah, Iraq
Hassan Kamil Jassim University of Thi-Qar, Department of Mathematics, 64001 Nasiriyah, Iraq
Ali Kareem Jassim Ministry of Education, Education Directorate of Thi-Qar, 64001 Nasiriyah, Iraq; National University of Science and Technology, College of Technical Engineering, 64001 Nasiriyah, Iraq

DOI:

https://doi.org/10.14311/AP.2024.64.0087

Keywords:

Volterra integral equations, new iterative method, Taylor series, Hussein Jassim method

Abstract

Many scientists have shown great interest in exploring the realm of second-kind integral equations, offering many techniques for solving them, including exact, approximate, and numerical methods. This paper introduces the Hussein-Jassim method (HJ-method) for solving Volterra integral equations of the second kind (VIESKs). The foundation of this approach lies in the principle of Maclaurin expansion. The algorithm of the method was derived, and its convergence was analysed. Furthermore, the method was applied to various Volterra integral equations, encompassing linear, nonlinear, homogeneous, and nonhomogeneous cases. Ultimately, the proposed method successfully addressed these equations, with the approximate solutions converging toward the exact solution.

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