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ADI schemes for higher-order nonlinear diffusion equations. (English) Zbl 1061.76051
Summary: Alternating direction implicit (ADI) schemes are constructed for 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 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 ADI schemes.

MSC:
76M20 Finite difference methods applied to problems in fluid mechanics
76A20 Thin fluid films
76R50 Diffusion
Software:
KELLEY
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