A computer‐assisted method for the diblock copolymer model
A computer‐assisted method for the diblock copolymer model
复制标题
二嵌段共聚物模型的计算机辅助方法
DOI：
10.1002/zamm.201800125
复制
发表时间：
2019
期刊：
影响因子：
--
通讯作者：
Watanabe Yoshitaka
中科院分区：
文献类型：
--
作者：
Cai Shuting;Watanabe Yoshitaka
我们提出了一种计算机辅助方法，通过该方法来封闭二嵌段共聚物模型的溶液。首先用牛顿法求出了一个解，然后证明了近似的残差部分是紧算子的不动点。其次，我们利用计算机构造了一个集合，该集合满足某Sobolev空间中算子的Banach不动点定理的假设，因此包含一个唯一解。最后给出了一些验证结果。
We propose a computer‐assisted method by which to enclose a solution of the diblock copolymer model. We begin by using the Newton method to obtain a solution, and we then prove that the residual part of the approximation is a fixed point of a compact operator. Next, using a computer, we construct a set which satisfies the hypothesis of the Banach fixed‐point theorem for the operator in a certain Sobolev space, which therefore contains a unique solution. Finally, we present some verified results.