Numerical Approach for Brain Tumor Growth Model Using Higher Order Compact Finite Difference Scheme

In this work, we develop a high-order finite difference framework for simulating brain tumor growth governed by a reaction-diffusion model with a spatially varying diffusion coefficient. The proposed scheme combines a fourth-order compact finite difference discretization in space with a second-order Crank-Nicolson method for time integration. The method attains fourth-order accuracy at interior grid points and second-order accuracy in time. Numerical convergence studies confirm second-order accuracy in time, while spatial experiments demonstrate an effective global spatial accuracy of order O\!( h3.6) due to boundary discretization effects. Overall, the method exhibits an accuracy of O\!( τ ² + h3.6). Compared with classical second-order finite difference schemes, the proposed approach reduces numerical diffusion and achieves comparable accuracy on coarser grids, enabling efficient long-time simulations. The resulting framework provides an accurate and computationally efficient tool for numerical studies of glioma growth.