Advanced tumor growth modeling: A numerical study integrating phase plane analysis with finite volume method

This study investigates tumor density dynamics through computational modeling, focusing on key parameters: proliferation rate m, diffusion coefficient τ, and additional factors c and κ. Systematic exploration reveals nuanced interactions shaping tumor growth, regression, and dispersal. Higher m values accelerate proliferation, while increased τ facilitates dispersal. Parameters c and κ further refine our understanding of tumor behavior. These insights inform the development of computational models for oncological research, with implications for targeted therapeutic interventions. The aim can be realized by utilizing the propose Finite Volume Method to develop a representation of cancer models and improve the efficiency of their simulations. Furthermore, the numerical results will be validated by comparing them with the Tanh-Coth method formulation to assess the model's accuracy and efficiency. The findings suggest that accurate modeling of tumor dynamics can aid in predicting tumor progression and response to treatments, ultimately contributing to personalized medicine and more effective therapeutic strategies. Phase plane analysis shows the schemes are conditionally stable and accurate to the fourth order in time. The method demonstrates exceptional agreement and error-free findings compared to 3D plots, underscoring its potential utility in clinical and research settings.