ADI schemes for higher-order nonlinear diffusion equations

T. P. Witelski*, M. Bowen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

121 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)331-351
Number of pages21
JournalApplied Numerical Mathematics
Issue number2-3
Publication statusPublished - 2003 May
Externally publishedYes


  • ADI methods
  • Approximate factorization
  • Higher-order equations
  • Nonlinear diffusion equations
  • Parabolic PDE

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics


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