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Orthogonal cubic spline collocation method for the Cahn–Hilliard equation

Danumjaya, P and Nandakumaran, AK (2006) Orthogonal cubic spline collocation method for the Cahn–Hilliard equation. In: Applied Mathematics and Computation, 182 (2). pp. 1316-1329.

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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.

Item Type: Journal Article
Publication: Applied Mathematics and Computation
Publisher: Elsevier
Additional Information: Copyright of this article belongs to Elsevier.
Keywords: Cahn–Hilliard equation;Orthogonal cubic spline collocation method;Lyapunov functional;A priori bounds;Optimal error estimates;Monomial basis functions;RADAU 5
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 31 Jan 2007
Last Modified: 19 Sep 2010 04:34
URI: http://eprints.iisc.ac.in/id/eprint/9637

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