A computer‐assisted method for the diblock copolymer model | Zendy

Cai Shuting | Zendy; Watanabe Yoshitaka | Zendy

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A computer‐assisted method for the diblock copolymer model

Author(s) -

Cai Shuting,

Watanabe Yoshitaka

Publication year - 2019

Publication title -

zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.449

H-Index - 51

eISSN - 1521-4001

pISSN - 0044-2267

DOI - 10.1002/zamm.201800125

Subject(s) - copolymer , operator (biology) , fixed point , set (abstract data type) , sobolev space , construct (python library) , point (geometry) , computer science , banach space , fixed point theorem , residual , mathematics , algorithm , pure mathematics , mathematical analysis , materials science , geometry , biochemistry , repressor , transcription factor , composite material , gene , programming language , polymer , chemistry

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.

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