TY - JOUR
T1 - ADI schemes for higher-order nonlinear diffusion equations
AU - Witelski, T. P.
AU - Bowen, M.
N1 - Funding Information:
We thank Andrea Bertozzi for suggesting this project and for many helpful conversations. This research was supported by NSF grant FRG-DMS 0074049 and ONR grant N-00140110290. TW was also supported by a fellowship from the Alfred P. Sloan Foundation.
Copyright:
Copyright 2004 Elsevier Science B.V., Amsterdam. All rights reserved.
PY - 2003/5
Y1 - 2003/5
N2 - 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.
AB - 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.
KW - ADI methods
KW - Approximate factorization
KW - Higher-order equations
KW - Nonlinear diffusion equations
KW - Parabolic PDE
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U2 - 10.1016/S0168-9274(02)00194-0
DO - 10.1016/S0168-9274(02)00194-0
M3 - Article
AN - SCOPUS:0037401623
SN - 0168-9274
VL - 45
SP - 331
EP - 351
JO - Applied Numerical Mathematics
JF - Applied Numerical Mathematics
IS - 2-3
ER -