In the present work, we introduce a new numerical method based on a strong version of the mean-value theorem for integrals to solve quadratic Volterra integral equations and Fredholm integral equations of the second kind, for which there are theoretical monotonic non-negative solutions. By means of an equality theorem, the integral that appears in the aforementioned equations is transformed into one that enables a more accurate numerical solution with fewer calculations than other previously described methods. Convergence analysis is given. (C) 2020 Elsevier B.V. All rights reserved.

De Angelis, P., De Marchis, R., Martire, A.L. (2020). A new numerical method for a class of Volterra and Fredholm integral equations. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 379, 112944 [10.1016/j.cam.2020.112944].

A new numerical method for a class of Volterra and Fredholm integral equations

Antonio Luciano Martire
2020-01-01

Abstract

In the present work, we introduce a new numerical method based on a strong version of the mean-value theorem for integrals to solve quadratic Volterra integral equations and Fredholm integral equations of the second kind, for which there are theoretical monotonic non-negative solutions. By means of an equality theorem, the integral that appears in the aforementioned equations is transformed into one that enables a more accurate numerical solution with fewer calculations than other previously described methods. Convergence analysis is given. (C) 2020 Elsevier B.V. All rights reserved.
De Angelis, P., De Marchis, R., Martire, A.L. (2020). A new numerical method for a class of Volterra and Fredholm integral equations. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 379, 112944 [10.1016/j.cam.2020.112944].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11590/425367
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