The main target of this paper is to present a new and efficient method to solve a nonlinear free boundary mathematical model of atherosclerosis. This model consists of three parabolic, one elliptic and one ordinary differential equations that are coupled together and describes the growth of a plaque in the artery. We start our discussion by using the front fixing method to fix the free domain and simplify the model by changing the mixed boundary condition to a Neumann one by applying suitable changes of variables. Then, after employing a finite difference using the second-order backward difference formula (BDF2) and the collocation method on this model, we prove the stability and convergence of methods. Finally, some numerical results are considered to show the efficiency of the method.

本文的主要目标是提出一种新的有效方法来求解动脉粥样硬化的非线性自由边界数学模型。该模型由三个抛物线形，一个椭圆形和一个常微分方程组成，它们耦合在一起并描述了动脉斑块的生长。我们通过使用前端固定方法固定自由域并通过应用变量的适当更改将混合边界条件更改为诺伊曼条件来简化模型，从而开始我们的讨论。然后，在该模型上使用二阶后向差分公式（BDF2）并采用搭配方法对有限差分进行了证明之后，我们证明了方法的稳定性和收敛性。最后，考虑了一些数值结果，表明了该方法的有效性。