Modeling of biological population problems using the element-free kp-Ritz method

A degenerate parabolic equation arising in the spatial diffusion of biological population is analyzed using the mesh-free kp-Ritz method. The mesh-free kernel particle estimate is employed to approximate the 2D displacement field. A system of discrete equations is obtained through application of the Ritz minimization procedure to the energy expressions. To validate the accuracy of the results and stability of the present method, convergence studies were carried out based on influences of support size and number of nodes. Effectiveness of the mesh-free kp-Ritz method for biological population model is investigated by numerical examples in this paper. The present results were compared with results reported in extant literature and were found to be in good agreement with the literature.