Alternating-direction implicit method: Difference between revisions

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In [[mathematics]], the '''alternating direction implicit (ADI) method''' is<ref>Peaceman, aD. [[finiteW. difference]]and methodRachford, forH. solvingH., differential equationsJr., "The Itnumerical is most notably used to solve the problemsolution of [[heatparabolic conduction]]and orelliptic solvingdifferential the [[diffusion equation]] in two or more dimensions.equations",

SIAM J. 3 (1955), 28-41, [http://www.ams.org/mathscinet-getitem?mr=71874 MR71874]</ref>is a [[finite difference]] method for solving parabolic and elliptic partial differential equations. It is most notably used to solve the problem of [[heat conduction]] or solving the [[diffusion equation]] in two or more dimensions.

The traditional method for solving the heat conduction equation is the method of [[Crank-Nicolson]]. This method is implicit, but has an unaffordable stability criterion in two or more dimensions.