ADI schemes for higher-order nonlinear diffusion equations

T. P. Witelski, Mark Bowen

Research output: Contribution to journalArticle

97 Citations (Scopus)

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 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
Volume45
Issue number2-3
DOIs
Publication statusPublished - 2003 May
Externally publishedYes

Fingerprint

Alternating Direction
Nonlinear Diffusion Equation
Implicit Scheme
Thin Film Equation
Higher Order
Approximate Factorization
Linear Diffusion
Thin films
Fourth-order Equations
Fluid Dynamics
Fluid dynamics
Iterative methods
Factorization
Surface Tension
Evolution Equation
Fluid Flow
Surface tension
Nonlinear Problem
Thin Films
Flow of fluids

Keywords

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

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics
  • Modelling and Simulation

Cite this

ADI schemes for higher-order nonlinear diffusion equations. / Witelski, T. P.; Bowen, Mark.

In: Applied Numerical Mathematics, Vol. 45, No. 2-3, 05.2003, p. 331-351.

Research output: Contribution to journalArticle

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