Numerical approach for brain tumor growth model using higher order compact finite difference scheme

In this article, we focus on analyzing the reaction-diffusion model applied to brain gliomas, incorporating two distinct types of growth functions. To gain a comprehensive understanding, we extend our analysis to different types of tissue environments. We explore scenarios where the diffusion coefficient remains constant, reflecting a homogeneous tissue environment. Additionally, we investigate cases where the diffusion coefficient becomes spatially variable, introducing heterogeneity into the model. This spatial variability accounts for the varying properties of different regions within the brain. Subsequently, we extend our investigation to heterogeneous tissue environments in $2$-dimensions. Our analysis of simulation results reveals differences in growth patterns based on the parameters utilized.