Encyclopedia of Applied and Computational Mathematics

2015 Edition
| Editors: Björn Engquist

ADI Methods

  • Qin Sheng
Reference work entry
DOI: https://doi.org/10.1007/978-3-540-70529-1_435

Mathematics Subject Classification

65M06; 65N06


Alternating direction implicit method; Splitting method


Finite-difference methods have been extremely important to the numerical solution of partial differential equations. An ADI method is one of them with extraordinary features in structure simplicity, computational efficiency, and flexibility in applications.

The original ADI idea was proposed by D. W. Peaceman and H. H. Rachford, Jr., [ 12] in 1955. Later, J. Douglas, Jr., and H. H. Rachford, Jr., [ 3] were able to implement the algorithm by splitting the time-step procedure into two fractional steps. The strategy of the ADI approach can be readily explained in a contemporary way of modern numerical analysis. To this end, we let \(\mathcal{D}\)
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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Qin Sheng
    • 1
  1. 1.Department of MathematicsBaylor UniversityWacoUSA