Numerical investigation based on the Chebyshev-HPM for Riccati/Logistic differential equations

M. M. Khader; A. M. Shloof; Halema Ali Hamead; M. M. Khader; A. M. Shloof; Halema Ali Hamead

doi:10.3934/math.2025363

AIMS Mathematics

2025, Volume 10, Issue 4: 7906-7919. doi: 10.3934/math.2025363

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Research article

Numerical investigation based on the Chebyshev-HPM for Riccati/Logistic differential equations

1.
Department of Mathematics and Statistics, College of Science, Imam Mohammad, Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia
2.
Department of Mathematics, Faculty of Science, University of Zintan, AlZintan, Libya
3.
Department of Mathematics, Faculty of Education, University of Aljufra, Aljufra, Libya

Received: 02 February 2025 Revised: 05 March 2025 Accepted: 14 March 2025 Published: 07 April 2025
MSC : 26A33, 34A08, 65N06, 65N12

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.
- Riccati/Logistic differential equation,
- homotopy perturbation method,
- Chebyshev expansion,
- Convergence analysis,
- RK4 method
Citation: M. M. Khader, A. M. Shloof, Halema Ali Hamead. Numerical investigation based on the Chebyshev-HPM for Riccati/Logistic differential equations[J]. AIMS Mathematics, 2025, 10(4): 7906-7919. doi: 10.3934/math.2025363

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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.

References

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