Theoretical Analysis and Approximate Solutions of Two-Dimensional Nonlinear Fredholm Integral Equations Using Adomian polynomials (ADM) and MATLAB
DOI:
https://doi.org/10.65405/k1tk6466Keywords:
Two-dimensional Fredholm integral equation , Adomian Decomposition Method, Approximate solution, Numerical solution, Absolute error.Abstract
In this paper, the existence and uniqueness of the solution for the two-dimensional non-linear Fredholm integral equation are established using the fixed-point theorem, incorporating Adomian's approximation and the Lipschitz condition. We derive the approximate analytical solution Using the Adomian polynomials (Adomian decomposition method( ADM)) and compare it directly with the exact solution using MATLAB. Furthermore, we present various cases solved both analytically and numerically, evaluating each against the exact solution. The findings demonstrate a rapid convergence rate for ADM, confirming its superior computational efficiency in Two-dimensions.
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References
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