Choudhary, Santosh KumarSen, ShuvamHosseini, KamyarDas, Hirak JyotiDehingia, Kaushik2026-04-212026-04-2120261402-92511776-085210.1007/s44198-026-00395-92-s2.0-105033456305https://hdl.handle.net/123456789/9072https://doi.org/10.1007/s44198-026-00395-9In 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(h(3.6)) due to boundary discretization effects. Overall, the method exhibits an accuracy of O(tau(2) + h(3.6)). 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.eninfo:eu-repo/semantics/openAccessCrank-Nicolson MethodDiffusionReaction-Diffusion ModelArticle