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 due to boundary discretization effects. Overall, the method exhibits an accuracy of. 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.