@article{Khader2025, 
author = {M. M. Khader and A. M. Shloof and Halema Ali Hamead},
title = {Numerical investigation based on the Chebyshev-HPM for Riccati/Logistic differential equations},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {4},
pages = {7906-7919},
keywords = {Riccati/Logistic differential equation, homotopy perturbation method, Chebyshev expansion, Convergence analysis, RK4 method},
url = {https://www.sciopen.com/article/10.3934/math.2025363},
doi = {10.3934/math.2025363},
abstract = {We give the approximate solution of the Riccati/Logistic differential equations (RDE/LDE). The suggested approach depends on the homotopy perturbation method developed with the Chebyshev series (CHPM). A study of the convergence analysis of CHPM is presented. The residual error function is calculated and used as a basic criterion in evaluating the accuracy and efficiency of the given numerical technique. We use the exact solution and the Runge-Kutta method of fourth order for comparison with the results of the method used. Through these results, we can confirm that the applied method is an easy and effective tool for the numerical simulation of such models. Illustrative models are given to confirm the validity and usefulness of the proposed procedure.}
}