High-order numerical solution for a class of nonlinear Fredholm integro-differential equations

Amiri, Sadegh; Eshaghnezhad, Mohammad

doi:10.22034/cmde.2024.58818.2489

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	High-order numerical solution for a class of nonlinear Fredholm integro-differential equations
Computational Methods for Differential Equations
مقاله 24، دوره 13، شماره 3، مهر 2025، صفحه 1059-1073 اصل مقاله (679.18 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2024.58818.2489
نویسندگان
Sadegh Amiri^* ؛ Mohammad Eshaghnezhad
Department of Basic Sciences, Shahid Sattari Aeronautical University of Science and Technology P.O. Box: 13846-63113, Tehran, Iran.
چکیده
The main objective of this work is to present a high-order numerical method to solve a class of nonlinear Fredholm integro-differential equations. By multiplying appropriate efficient factors and constructing an appropriate approximate function, as well as employing a numerical integration method of order $\gamma$, the above-mentioned problem can be simplified to a nonlinear system of algebraic equations. Furthermore, we discuss the convergence analysis of the presented method in detail and demonstrate that it converges with an order $\mathcal{O}(h^{3.5})$ in the $L^2$-norm. Some test examples are provided to demonstrate that the claimed order of convergence is obtained.
کلیدواژه‌ها
Efficient factors؛ Approximate function؛ Nonlinear algebraic system؛ Convergence analysis؛ Order of convergence

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High-order numerical solution for a class of nonlinear Fredholm integro-differential equations