Numerical simulation of a degenerate parabolic problem occurring in the spatial diffusion of biological population

O. Nikan, Z. Avazzadeh*, J. A. Tenreiro Machado

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)

Abstract

This paper studies a localized meshless algorithm for calculating the solution of a nonlinear biological population model (NBPM). This model describes the dynamics in the biological population and may provide valuable predictions under different scenarios. The solution of the NBPM is approximated by means of local radial basis function based on the partition of unity (LRBF-PU) technique. First, the partial differential equation (PDE) is converted into a system of ordinary differential equations (ODEs) with the help of radial kernels. Afterwards, the system of ODEs is solved through an ODE solver of high-order. The major advantage of this scheme is that it does not requires any linearization. The LRBF-PU approximation helps handling the issue of the matrix ill conditioning that arises in a global RBF approximation. Three examples highlight the efficiency and accuracy of the numerical method. It is verified that the proposed strategy is more efficient in terms of computational time and accuracy in comparison with others available in the literature.

Original languageEnglish
Article number111220
JournalChaos, Solitons and Fractals
Volume151
DOIs
Publication statusPublished - Oct 2021

Keywords

  • LRBF-PU
  • Meshless method
  • Nonlinear Biological population model
  • RBF
  • Shape parameter

Fingerprint

Dive into the research topics of 'Numerical simulation of a degenerate parabolic problem occurring in the spatial diffusion of biological population'. Together they form a unique fingerprint.

Cite this