Journal
APPLIED NUMERICAL MATHEMATICS
Volume 45, Issue 2-3, Pages 331-351Publisher
ELSEVIER
DOI: 10.1016/S0168-9274(02)00194-0
Keywords
ADI methods; nonlinear diffusion equations; parabolic PDE; approximate factorization; higher-order equations
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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. (C) 2002 IMACS. Published by Elsevier Science B.V. All rights reserved.
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