Integrating factor‐based time integrators for the Cahn–Hilliard equation

Abstract

In this paper, we propose integrating factor (IF)‐based methods for solving the Cahn–Hilliard (CH) equation, which was originally proposed to describe the phase separation phenomenon for binary melted alloy below the critical temperature, and since then, it has appeared in many fields. Being a nonlinear equation, it is of great importance to develop efficient numerical methods for investigating the solution behavior of the CH equation. We present a few important linear and nonlinear schemes for the CH equation and obtain error estimates for those schemes. The integrators that we present here are of first and second order in time. We show numerical results to illustrate our theoretical findings.