TY - JOUR
T1 - Analytical and numerical treatment of a nonlinear Fredholm integral equation in two dimensions
AU - Alahmadi, Jihan
AU - Abdou, M. A.
AU - Abdel-Aty, M. A.
N1 - Publisher Copyright:
© The Author(s) under exclusive licence to Korean Society for Informatics and Computational Applied Mathematics 2024.
PY - 2025/4
Y1 - 2025/4
N2 - In this article, we have analytically proven that the integral equation in two dimensions (IE-TD) of the second type has at least one solution by using Tychonoff’s fixed point theorem. Then, the Adomian decomposition method (ADM) was used to solve the IE-TD, and the convergence of the method was also proved. Moreover, we utilized the Homotopy analysis method (HAM) to get the solution of the IE-TD, and the method’s convergence was investigated. The effectiveness and preciseness of the proposed approaches were illustrated using numerical examples, and the error estimate for each case was calculated. Finally, conclusions are obtained.
AB - In this article, we have analytically proven that the integral equation in two dimensions (IE-TD) of the second type has at least one solution by using Tychonoff’s fixed point theorem. Then, the Adomian decomposition method (ADM) was used to solve the IE-TD, and the convergence of the method was also proved. Moreover, we utilized the Homotopy analysis method (HAM) to get the solution of the IE-TD, and the method’s convergence was investigated. The effectiveness and preciseness of the proposed approaches were illustrated using numerical examples, and the error estimate for each case was calculated. Finally, conclusions are obtained.
KW - Adomian decomposition method
KW - Homotopy analysis method
KW - Integral equation in two dimensions
KW - Tychonoff’s fixed point theorem
UR - http://www.scopus.com/inward/record.url?scp=105002985840&partnerID=8YFLogxK
U2 - 10.1007/s12190-024-02264-4
DO - 10.1007/s12190-024-02264-4
M3 - Article
AN - SCOPUS:105002985840
SN - 1598-5865
VL - 71
SP - 1693
EP - 1719
JO - Journal of Applied Mathematics and Computing
JF - Journal of Applied Mathematics and Computing
IS - 2
ER -