A numerical method based on the boundary integral equation and dual reciprocity methods for one-dimensional Cahn-Hilliard equation

Abstract

This paper describes a numerical method based on the boundary integral equation and dual reciprocity methods for solving the one-dimensional Cahn-Hilliard (C-H) equation. The idea behind this approach comes from the dual reciprocity boundary element method that introduced for higher order dimensional problems. A time-stepping method and a predictor-corrector scheme are employed to deal with the time derivative and the nonlinearity respectively. Numerical results are presented for some examples to demonstrate the usefulness and accuracy of this approach. For these problems the energy functional dissipation and the mass conservation properties are investigated. © 2008 Elsevier Ltd. All rights reserved.