An improved element-free Galerkin method for numerical modeling of the biological population problems

A numerical study is performed for degenerate parabolic equations arising from the spatial diffusion of biological populations based on the improved element-free Galerkin (IEFG) method. Using the IEFG technique, a discrete equation system for the biological problem is derived via the Galerkin procedure, and the penalty method is employed to impose the essential boundary conditions. In this study, the applicability of the IEFG method for biological population problems is examined through a number of numerical examples. In general, the initial and boundary conditions of the biological population problems are time dependent; therefore, it is necessary to carry out convergence studies by varying the number of nodes and time steps in order to establish the convergent solutions. The IEFG solutions obtained for the examples are compared with the results reported in the extant literature and they found to be in close agreement.