| Autor: |
Mohammad, Najem A., Sabawi, Younis A., Hasso, Mohammad Sh. |
| Zdroj: |
Palestine Journal of Mathematics; 2024, Vol. 13 Issue 3, p354-370, 17p |
| Abstrakt: |
The main focus of this paper is to introduce and analyze numerical methods for solving nonlinear Fredholm integro-differential equations. Two specific methods, namely homotopy perturbation and variational iteration methods, are implemented in this study. To assess the accuracy of the proposed schemes, extensive computational testing is conducted. The convergence analysis is performed using contracting mapping, which is a common method for proving the convergence of iterative algorithms. Additionally, the paper explores the error bound of an approximate solution generated from the partial sum of the series. This provides insights into the quality of the approximation.Comparison studies between the proposed methods are also carried out to evaluate their performance. The accuracy of the methods is assessed through numerical examples and compared against existing solutions. To further analyze the errors, l∞ and l2 norms are used. These norms quantify the differences between the approximate and actual solutions, providing a measure of accuracy. Finally, the efficiency of the approach is evaluated, considering factors such as computational complexity and execution time. The results of the numerical experiments are compared with previous studies and analytical solutions to validate their reliability and compatibility. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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