In this paper, we introduce a new numerical procedure to solve multi-dimensional Volterra integral equations, based on the weighted mean-value theorem. Our method allows to determine a system of nonlinear equations, where the rst one is obtained via the application of the theoretical results, and the remaining ones are built through a Picard-like iterative algorithm. To test the soundness of our proposal, we compare the true and the approximate solutions for several examples.
A numerical method for multidimensional Volterra integral equations / Oliva, Immacolata; Luciano Martire, Antonio. - In: APPLIED MATHEMATICAL SCIENCES. - ISSN 1314-7552. - 16:12(2022), pp. 709-717. [10.12988/ams.2022.917306]
A numerical method for multidimensional Volterra integral equations
Immacolata Oliva;Antonio Luciano Martire
2022
Abstract
In this paper, we introduce a new numerical procedure to solve multi-dimensional Volterra integral equations, based on the weighted mean-value theorem. Our method allows to determine a system of nonlinear equations, where the rst one is obtained via the application of the theoretical results, and the remaining ones are built through a Picard-like iterative algorithm. To test the soundness of our proposal, we compare the true and the approximate solutions for several examples.| File | Dimensione | Formato | |
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