| Publications [#10446] of Thomas P. Witelski
search www.ams.org.Papers Published
- Thomas P. Witelski and M. Bowen, ADI schemes for fourth-order nonlinear diffusion equations,
Applied Numerical Mathematics, vol. 45 no. 2-3
(2003),
pp. 331-351 [S0168-9274(02)00194-0]
(last updated on 2004/02/12)
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
for the solution of nonlinear problems. Problems in the
fluid dynamics of thin films are solved to demonstrate the
effectiveness of the ADI schemes.
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