TY - JOUR AU - Abdou, M. A. AU - Youssef, M. I. PY - 2022 TI - On a method for solving nonlinear integro differential equation of order $n$ JO - Journal of Mathematics and Computer Science SP - 322--340 VL - 25 IS - 4 AB - This work is concerned with the study of a general class of nonlinear integro-differential equations of order n. Using a suitable transformation, we derive an equivalent nonlinear Fredholm-Volterra integral equation (NF-VIE) to this class of equations. The existence of continuous solutions for the NF-VIE is investigated subject to the verification of some sufficient conditions. We apply the modified Adomian's decomposition method (MADM) and homotopy analysis method (HAM) to solve this NF-VIE. The convergence and error estimate of the approximate solution are also studied. The numerical results in this article show that the HAM technique may give an approximate solution with high accuracy and convergence rate faster than the one obtained using the MADM technique provided the convergence control parameter \(\hbar\) is properly chosen when applying the HAM. SN - ISSN 2008-949X UR - http://dx.doi.org/10.22436/jmcs.025.04.03 DO - 10.22436/jmcs.025.04.03 ID - Abdou2022 ER -