New alternative numerical approaches for solving the glioma model and their efficiencies

Abstract

In this article, the numerical solution of glioma, or glioblastomas, which is one of the most aggressive forms of cancer is considered. A heterogeneous nonlinear diffusion logistic density model is taken as the main focus. To obtain the numerical results, three different discretization techniques: Pseudospectral method (PSM) using Chebyshev–Gauss–Lobatto collocation points, method of lines (MoL), and cubic B-splines (cBS) are employed on the spatial domain, whereas 4th-order Runge–Kutta (RK4) is considered on the time domain. Adapting cBS and PSM discretization to the glioma model is studied at first in this study. In addition to the theoretical convergence results, detailed comparative computational results are presented. All these methods are compared in terms of their efficiencies in varying time step and mesh discretization not only to one another, but also with the methods given in the literature.