The first half of this work develops and analyzes the Shortley–Weller scheme (or<br>Ghost-Fluid method with quadratic extrapolation) for a two-point boundary value<br>problem with variable coefficients, where the boundary points are not on the uniform<br>mesh. We prove that the local truncation error is first order convergent near the<br>boundary, but the solution is third order accurate near the boundary and second order<br>accurate away from the boundary. The second half of this work applies this numerical<br>scheme to investigate the tumor growth problems in heterogeneous microenvironment.<br>We discover that the classic Darcy’s law tumor model can capture the chemotaxis<br>property using variable nutrient diffusion rate and the haptotaxis mechanism through<br>the variable extracellular matrix (ECM) permeability. Specifically, the tumor tends to<br>move to the regions with higher diffusion rate or lower ECM permeability.
|Journal||Journal of Computational and Applied Mathematics|
|State||Published - Oct 2020|