A computer‐assisted method for the diblock copolymer model. Issue 7 (24th April 2019)

• Record Type: Journal Article
• Authors: Cai, Shuting; Watanabe, Yoshitaka
• Is Part Of: Zeitschrift für angewandte Mathematik und Mechanik. Volume 99:Issue 7(2019)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2019-04-24
• Subjects: Banach fixed‐point theorem -- computer‐assisted method -- diblock copolymer; Mathematics -- Periodicals; Mechanics, Applied -- Periodicals; Engineering -- Periodicals; 519
• DOI: 10.1002/zamm.201800125
• Languages: English
• ISSNs: 0044-2267

Abstract

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. 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.