In this paper, we present a novel and exible numerical method to solvenon-standard Volterra integral equations of the second kind. Starting from the mean-value theorem for integrals we give theoretical results that allow associating to each Volterra integral equation a system of non-linear equations that is solved by mean of a numerical method. The algorithm produces very accurate numerical solutions and it is very fast. To test the tness of our method, we applied it to some examples.
Non-standard Volterra integral equations: a mean-value theorem numerical approach / DE ANGELIS, Paolo; DE MARCHIS, Roberto; Martire, ANTONIO LUCIANO; Patri', Stefano. - In: APPLIED MATHEMATICAL SCIENCES. - ISSN 1312-885X. - 14:9(2020), pp. 423-432. [10.12988/ams]
Non-standard Volterra integral equations: a mean-value theorem numerical approach
Paolo De Angelis;Roberto De Marchis;Antonio Luciano Martire
;Stefano Patrì
2020
Abstract
In this paper, we present a novel and exible numerical method to solvenon-standard Volterra integral equations of the second kind. Starting from the mean-value theorem for integrals we give theoretical results that allow associating to each Volterra integral equation a system of non-linear equations that is solved by mean of a numerical method. The algorithm produces very accurate numerical solutions and it is very fast. To test the tness of our method, we applied it to some examples.| File | Dimensione | Formato | |
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