### 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 language | English |
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Article number | e201800125 |

Journal | ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik |

Volume | 99 |

Issue number | 7 |

DOIs | |

Publication status | Published - Jul 1 2019 |

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### 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.

Research output: Contribution to journal › Article

*ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik*, vol. 99, no. 7, e201800125. https://doi.org/10.1002/zamm.201800125

}

TY - JOUR

T1 - A computer-assisted method for the diblock copolymer model

AU - Cai, Shuting

AU - Watanabe, Yoshitaka

PY - 2019/7/1

Y1 - 2019/7/1

N2 - 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.

AB - 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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UR - http://www.scopus.com/inward/citedby.url?scp=85065023590&partnerID=8YFLogxK

U2 - 10.1002/zamm.201800125

DO - 10.1002/zamm.201800125

M3 - Article

AN - SCOPUS:85065023590

VL - 99

JO - ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik

JF - ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik

SN - 0044-2267

IS - 7

M1 - e201800125

ER -