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Collocation method using auto-correlation functions of compact supported wavelets for solving Volterra’s population model

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  • Alipanah, Amjad
  • Zafari, Mahnaz

Abstract

In this paper, we present two numerical collocation methods for approximating the solution of Volterra’s population model by utilizing auto-correlation functions of scaling functions of Daubechies wavelets. By using the properties of these functions, we compute the Volterra integral exactly at dyadic points, and then reduce the integro-differential population model to a system of algebraic equations. Our numerical results demonstrate the effectiveness and accuracy of these methods, and we compare our numerical results with other approaches described in the literature. Additionally, we investigate an error bound for our schemes.

Suggested Citation

  • Alipanah, Amjad & Zafari, Mahnaz, 2023. "Collocation method using auto-correlation functions of compact supported wavelets for solving Volterra’s population model," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    • Handle: RePEc:eee:chsofr:v:175:y:2023:i:p1:s0960077923008421
    DOI: 10.1016/j.chaos.2023.113941
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    References listed on IDEAS

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    1. Amjad Alipanah & Korosh Arzideh & Medina Firouzi & A. Kasnazani & Marianna A. Shubov, 2022. "Daubechies Wavelet Scaling Function Approach to Solve Volterra’s Population Model," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2022, pages 1-8, September.
    2. Ramezani, M. & Razzaghi, M. & Dehghan, M., 2007. "Composite spectral functions for solving Volterra’s population model," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 588-593.
    3. He, Ji-Huan, 2005. "Application of homotopy perturbation method to nonlinear wave equations," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 695-700.
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