Orthogonal cubic spline collocation method for the Cahn–Hilliard equation

Abstract

The Cahn–Hilliard equation plays an important role in the phase separation in a binary mixture. This is a fourth order nonlinear partial differential equation. In this paper, we study the behaviour of the solution by using orthogonal cubic spline collocation method and derive optimal order error estimates. We discuss some computational experiments by using monomial basis functions in the spatial direction and RADAU 5 time integrator. The method we present here is better in terms of stability, efficiency and conditioning of the resulting matrix. Since no integrals to be evaluated or approximated, it behaves better than finite element method.