ADI schemes for higher-order nonlinear diffusion equations

Authors:
T. P. Witelski;M. Bowen
Affiliations:
Department of Mathematics and the Center for Nonlinear and Complex Systems, Duke University, Durham, NC;School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK
Venue:
Applied Numerical Mathematics
Year:
2003

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Abstract

Alternating Direction Implicit (ADI) schemes are constructed for the solution of two-dimensional higher-order linear and nonlinear diffusion equations, particularly including the fourth-order thin film equation for surface tension driven fluid flows. First and second-order accurate schemes are derived via approximate factorization of the evolution equations. This approach is combined with iterative methods to solve nonlinear problems. Problems in the fluid dynamics of thin films are solved to demonstrate the effectiveness of the ADI schemes.