An IMEX scheme for a nonlinear PDE model of tumor angiogenesis

This paper presents a numerical analysis of an Implicit–Explicit scheme for a non-linear parabolic PDE model of tumor angiogenesis. The model describes the evolution of endothelial cells, proteases, inhibitors, and extracellular matrix through coupled equations incorporating diffusion, chemotaxis, haptotaxis, and reaction kinetics. We design a numerical approach that manages stiff linear terms implicitly while handling non-stiff nonlinear terms explicitly. Theoretical analysis establishes main features of the scheme such as stability properties, second-order convergence, and preservation of conservation laws. Moreover, the computational complexity is analyzed, demonstrating an efficiency gains compared to fully explicit methods. Numerical experiments validate these findings and show the ability of the method to accurately capture complex biological phenomena.