A computer-assisted method for the diblock copolymer model

Shuting Cai, Yoshitaka Watanabe

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish
Article numbere201800125
JournalZAMM Zeitschrift fur Angewandte Mathematik und Mechanik
Volume99
Issue number7
DOIs
Publication statusPublished - Jul 1 2019

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Copolymer
Block copolymers
Banach Fixed Point Theorem
Sobolev spaces
Compact Operator
Newton-Raphson method
Newton Methods
Unique Solution
Sobolev Spaces
Mathematical operators
Fixed point
Approximation
Operator
Model

All Science Journal Classification (ASJC) codes

  • Computational Mechanics
  • Applied Mathematics

Cite this

A computer-assisted method for the diblock copolymer model. / Cai, Shuting; Watanabe, Yoshitaka.

In: ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik, Vol. 99, No. 7, e201800125, 01.07.2019.

Research output: Contribution to journalArticle

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