- Thomas P. Witelski and M. Bowen, ADI schemes for fourth-order nonlinear diffusion equations,
Applied Numerical Mathematics, vol. 45 no. 2-3
pp. 331-351 [S0168-9274(02)00194-0] .
(last updated on 2004/02/12)
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.