TY - GEN
T1 - The Quotient Homotopy Analysis Method for Solving Nonlinear Initial Value Problems
AU - Oudetallah, Jamal
AU - Bahia, Ghenaiet
AU - Ouannas, Adel
AU - Batiha, Iqbal M.
N1 - Publisher Copyright:
© 2021 IEEE.
PY - 2021/7/14
Y1 - 2021/7/14
N2 - This article proposes a novel version of the popular method from the ever-so-famous homotopy analysis methods, namely Quotient Homotopy Analysis Method or simply QHAM, in order to provide numerical solutions for nonlinear initial value problems. The basic approach of this method relies firstly on constructing a suitable homotopy equation so that its solution will be then established in the form of a quotient of two formulated power series which will, in its turn, be the basis stone of the general numerical solution for the nonlinear problems. Two numerical comparisons via two examples are performed between the exact solution and the approximate numerical solution to reveal the importance and potential role of the established method in this work.
AB - This article proposes a novel version of the popular method from the ever-so-famous homotopy analysis methods, namely Quotient Homotopy Analysis Method or simply QHAM, in order to provide numerical solutions for nonlinear initial value problems. The basic approach of this method relies firstly on constructing a suitable homotopy equation so that its solution will be then established in the form of a quotient of two formulated power series which will, in its turn, be the basis stone of the general numerical solution for the nonlinear problems. Two numerical comparisons via two examples are performed between the exact solution and the approximate numerical solution to reveal the importance and potential role of the established method in this work.
KW - Homotopy analysis method
KW - Riccati's nonlinear differential equation
KW - power series solution
UR - https://www.scopus.com/pages/publications/85112192612
U2 - 10.1109/ICIT52682.2021.9491751
DO - 10.1109/ICIT52682.2021.9491751
M3 - Conference contribution
AN - SCOPUS:85112192612
T3 - 2021 International Conference on Information Technology, ICIT 2021 - Proceedings
SP - 195
EP - 199
BT - 2021 International Conference on Information Technology, ICIT 2021 - Proceedings
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2021 International Conference on Information Technology, ICIT 2021
Y2 - 14 July 2021 through 15 July 2021
ER -