Error analysis of finite difference/collocation method for the nonlinear coupled parabolic free boundary problem modeling plaque growth in the artery

• A nonlinear coupled parabolic free boundary problem modeling plaque growth in the artery, using finite difference-collocation method, is solved. We have fixed domain front fixing method and model simplified by changing mixed condition to a Neumann one applying suitable change of variables achieve more comfortable results for numerical analysis. Applying difference second order backward formula (BDF2), we constructed sequence, which converges exact solution partial differential equations. In each time step, Taylor theorem, has changed linear collocation solved numerically convergence studied. proved sequence also stability proven. Some illustrative examples are employed showing efficiency presented method. simulated methods some pair initial concentrations LDL HDL blood show validity The main target this paper present new efficient solve mathematical atherosclerosis. This consists three parabolic, elliptic ordinary equations that together describes artery. start our discussion fix simplify changes variables. Then, after employing second-order (BDF2) on model, prove methods. Finally, considered