Numerical approximation for viscous Cahn–Hilliard equation via septic B-spline

Abstract

In this paper, a numerical technique is proposed for solving the nonlinear viscous Cahn–Hilliard equation. First, we obtain a time discrete scheme by approximating time derivative via a finite difference formula, then we use the interpolating septic B-spline approach to approximate the spatial derivative. The convergence of the method is considered, and the theoretical results are supported by numerical examples. We compare our numerical results with those given in the literature in terms of numerical accuracy. The numerical comparisons show that the presented method provides highly accurate results.

COMMUNICATED BY:

• C. Bacuta

Keywords:

• Viscous Cahn–Hilliard equation
• septic B-spline
• collocation
• finite difference
• convergence

2010 Mathematics Subject Classifications:

• 65M06
• 65M12
• 65M15

Acknowledgments

The author would like to express his thanks to the editor and unknown referee(s) for their careful reading, helpful comments and valuable suggestions, which help to improve this manuscript significantly.

Disclosure statement

No potential conflict of interest was reported by the author.