On existence and numerical solution of a new class of nonlinear second degree integro-differential Volterra equations with a convolution kernel
Samir Lemita1,2, Mohammed Lamine Guessoumi3
1Department of Mathematics and Computer Science, Echahid Cheikh Larbi Tebessi University, Tebessi, Algeria
2Laboratoire de Mathematiques Appliquees et de Modelisation, Universite 8 Mai 1945, Guelma, Algerie
3Departement des Sciences Exactes, Ecole Normale Superieure de Ouargla, Ouargla, Algerie
Keywords: Volterra equation, integro-differential equation, convolution kernel, Schauder fixed point theorem, Nystrőm method
Abstract
This paper considers a new class of nonlinear second degree integro-differential Volterra equations with a convolution kernel. We derive some sufficient conditions to establish the existence and uniqueness of solutions by using the Schauder fixed point theorem. Moreover, the Nystrőm method is applied to obtain an approximate solution of the proposed Volterra equation. Numerical examples are given to validate the adduced results.
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