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<p>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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathcal {O}\!\left( h^{3.6}\right)\)</EquationSource> </InlineEquation> due to boundary discretization effects. Overall, the method exhibits an accuracy of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathcal {O}\!\left( \tau ^{2} + h^{3.6}\right)\)</EquationSource> </InlineEquation>. 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.</p>

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

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年2月28日

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  • Hirak Jyoti Das,
  • Shuvam Sen,
  • Kaushik Dehingia,
  • Kamyar Hosseini,
  • Santosh Kumar Choudhary

摘要

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 \(\mathcal {O}\!\left( h^{3.6}\right)\) due to boundary discretization effects. Overall, the method exhibits an accuracy of \(\mathcal {O}\!\left( \tau ^{2} + h^{3.6}\right)\) . 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.