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Solving nonlinear Volterra-Fredholm integral equations using an accurate spectral collocation method

In: Tatra Mountains Mathematical Publications, vol. 80, no. 3
Fatima Hamani - Azedine Rahmoune

Details:

Year, pages: 2021, 35 - 52
Language: eng
Keywords:
Jacobi collocation methods, convergence analysis, spectral methods, nonlinear Volterra-Fredholm integral equations
Article type: Mathematics
Document type: scientific paper
About article:
In this paper, we present a Jacobi spectral collocation method to solve nonlinear Volterra-Fredholm integral equations with smooth kernels. The main idea in this approach is to convert the original problem into an equivalent one through appropriate variable transformations so that the resulting equation can be accurately solved using spectral collocation at the Jacobi-Gauss points. The convergence and error analysis are discussed for both $L$ and weighted $L2$ norms. We confirm the theoretical prediction of the exponential rate of convergence by the numerical results which are compared with well-known methods.
How to cite:
ISO 690:
Hamani, F., Rahmoune, A. 2021. Solving nonlinear Volterra-Fredholm integral equations using an accurate spectral collocation method. In Tatra Mountains Mathematical Publications, vol. 80, no.3, pp. 35-52. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2021-0030

APA:
Hamani, F., Rahmoune, A. (2021). Solving nonlinear Volterra-Fredholm integral equations using an accurate spectral collocation method. Tatra Mountains Mathematical Publications, 80(3), 35-52. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2021-0030
About edition:
Publisher: Mathematical Institute, Slovak Academy of Sciences, Bratislava
Published: 20. 12. 2021
Rights:
https://creativecommons.org/licenses/by-nc-nd/4.0/