An accelerated numerical framework to simulate brain tumor growth via KSOR method

The complex and invasive dynamics of brain tumours present significant clinical and computational challenges. This study aims to enhance the numerical efficiency of brain tumour growth simulation through an improved iterative solver. A two-dimensional diffusion–proliferation model of brain tumour growth is discretized using an implicit finite difference scheme to generate a large, sparse linear system. The resulting system is solved iteratively using the Kaudd Successive Over-Relaxation (KSOR) method and compared with the classical Gauss–Seidel (GS) approach in terms of convergence rate, iteration count, computation time, and numerical accuracy. Numerical experiments reveal that the KSOR method achieves up to 94.65% reduction in iterations and 86.33% faster computation compared to GS while maintaining high stability and accuracy. These findings demonstrate that integrating the implicit finite difference scheme with KSOR provides a robust and efficient numerical framework for modelling two-dimensional brain tumour dynamics. This approach offers practical implications for improving computational modelling of tumour progression, potentially supporting real-time prediction and treatment planning in biomedical and clinical applications.