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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.