Implementation of Crank-Nicolson scheme in cell dynamics simulation for diblock copolymers

Abstract

Many computational techniques have been designed to study block copolymer systems. Cell Dynamics Simulation (CDS) technique is one of those. It is based on solving partial differential equations (PDEs) and is computationally very fast compared to other simulation methods. In this contribution the focus is made on finite difference schemes and their use in computer simulation of PDEs involved in diblock copolymers systems. The Crank-Nicolson (CN) scheme of finite difference method is implemented in CDS method. The CN scheme is unconditionally stable but slower compared to Forward Euler's method which is fast but not very stable.