On a method for solving nonlinear integro differential equation of order $n$
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Authors
M. A. Abdou
- Department of Mathematics, Faculty of Education , Alexandria University, Alexandria, 21526, Egypt.
M. I. Youssef
- Department of Mathematics, College of Science, Jouf University, P. O. Box 2014, Sakaka, Saudi Arabia.
- Department of Mathematics, Faculty of Education, Alexandria University, Alexandria, 21526, Egypt.
Abstract
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.
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ISRP Style
M. A. Abdou, M. I. Youssef, On a method for solving nonlinear integro differential equation of order $n$, Journal of Mathematics and Computer Science, 25 (2022), no. 4, 322--340
AMA Style
Abdou M. A., Youssef M. I., On a method for solving nonlinear integro differential equation of order $n$. J Math Comput SCI-JM. (2022); 25(4):322--340
Chicago/Turabian Style
Abdou, M. A., Youssef, M. I.. "On a method for solving nonlinear integro differential equation of order $n$." Journal of Mathematics and Computer Science, 25, no. 4 (2022): 322--340
Keywords
- Integro-differential equations
- existence
- uniqueness
- modified Adomian's decomposition method
- homotopy analysis method
MSC
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