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.
Amiri, S. and Eshaghnezhad, M. (2025). High-order numerical solution for a class of nonlinear Fredholm integro-differential equations. Computational Methods for Differential Equations, 13(3), 1059-1073. doi: 10.22034/cmde.2024.58818.2489
MLA
Amiri, S. , and Eshaghnezhad, M. . "High-order numerical solution for a class of nonlinear Fredholm integro-differential equations", Computational Methods for Differential Equations, 13, 3, 2025, 1059-1073. doi: 10.22034/cmde.2024.58818.2489
HARVARD
Amiri, S., Eshaghnezhad, M. (2025). 'High-order numerical solution for a class of nonlinear Fredholm integro-differential equations', Computational Methods for Differential Equations, 13(3), pp. 1059-1073. doi: 10.22034/cmde.2024.58818.2489
CHICAGO
S. Amiri and M. Eshaghnezhad, "High-order numerical solution for a class of nonlinear Fredholm integro-differential equations," Computational Methods for Differential Equations, 13 3 (2025): 1059-1073, doi: 10.22034/cmde.2024.58818.2489
VANCOUVER
Amiri, S., Eshaghnezhad, M. High-order numerical solution for a class of nonlinear Fredholm integro-differential equations. Computational Methods for Differential Equations, 2025; 13(3): 1059-1073. doi: 10.22034/cmde.2024.58818.2489
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