A computer‐assisted method for the diblock copolymer model. Issue 7 (24th April 2019) - Cai, Shuting; Watanabe, Yoshitaka
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.