The aim of this paper is to establish conditions for the existence and uniqueness of the solution of a nonlinear integro-differential equation. Moreover, it is to propose a quadrature method in order to find an approximate solution and establish the convergence of the method. We conclude by providing the algorithm and some numerical simulation to confirm our theoretical results.
Nonlinear integro-differential equation, existence and uniqueness, Gauss-Kronrod, quadrature method, backward difference
RAMDANI, NEDJEM EDDINE and PINELAS, SANDRA
"Solving nonlinear integro-differential equations using numerical method,"
Turkish Journal of Mathematics: Vol. 46:
2, Article 22.
Available at: https://journals.tubitak.gov.tr/math/vol46/iss2/22