finite difference /配置法求解非线性耦合抛物型自由边界问题的误差分析
Error analysis of finite difference/collocation method for the nonlinear coupled parabolic free boundary problem modeling plaque growth in the artery
摘要：
本文的主要目的是提出一种新的有效的方法来求解动脉粥样硬化的非线性自由边界数学模型。该模型由三个抛物方程、一个椭圆方程和一个常微分方程组成，它们耦合在一起并描述动脉中斑块的生长。我们首先用波前固定法来固定自由区域，并通过适当的变量变换将混合边界条件变为Neumann边界条件来简化模型。然后，通过对该模型采用非经典差分和配置法，证明了方法的稳定性和收敛性。最后，一些数值结果被认为是显示该方法的有效性。
英文摘要：
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 parabolics, one elliptic and one ordinary differential equations that are coupled together and describe 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 mix boundary condition to a Neumann one by applying suitable changes of variables. Then, after employing a nonclassical finite difference 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.
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