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

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. (c) 2021 Elsevier Ltd. All rights reserved.

Automated summary

This paper presents a localized meshless algorithm for solving a nonlinear biological population model, using local radial basis function approximation to handle the dynamics of biological population and avoid matrix ill conditioning in global RBF approximations. The proposed strategy shows superior efficiency in terms of computational time and accuracy compared to other methods in the literature.