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=== Relations to other implicit methods ===
Many classical implicit methods by Peaceman-Rachford, Douglas-Gunn, D'Yakonov, Beam-Warming, Crank-Nicolson, etc., may be simplified to fundamental implicit schemes with operator-free right-hand sides.<ref name=":8" /> In their fundamental forms, the FADI method of second-order temporal accuracy can be related closely to the fundamental locally one-dimensional (FLOD) method, which can be upgraded to second-order temporal accuracy, such as for three-dimensional Maxwell's equations <ref>{{Cite journal|last=Tan|first=E. L.|date=2007|title=Unconditionally Stable LOD-FDTD Method for 3-D Maxwell's Equations|url=https://www.ntu.edu.sg/home/eeltan/papers/2007%20Unconditionally%20Stable%20LOD-FDTD%20Method%20for%203-D%20Maxwell’s%20Equations.pdf|journal=IEEE Microwave and Wireless Components Letters|volume=17|issue=2|pages=85–87|doi=10.1109/LMWC.2006.890166|hdl=10356/138296 |s2cid=22940993}}</ref><ref>{{Cite journal|last1=Gan|first1=T. H.|last2=Tan|first2=E. L.|date=2013|title=Unconditionally Stable Fundamental LOD-FDTD Method with Second-Order Temporal Accuracy and Complying Divergence|url=https://www.ntu.edu.sg/home/eeltan/papers/2013%20Unconditionally%20Stable%20Fundamental%20LOD-FDTD%20Method%20With%20Second-Order%20Temporal%20Accuracy%20and%20Complying%20Divergence.pdf|journal=IEEE Transactions on Antennas and Propagation|volume=61|issue=5|pages=2630–2638|doi=10.1109/TAP.2013.2242036|bibcode=2013ITAP...61.2630G|s2cid=7578037}}</ref> in [[computational electromagnetics]]. For two- and three-dimensional heat conduction and diffusion equations, both FADI and FLOD methods may be implemented in simpler, more efficient and stable manner compared to their conventional methods.<ref>{{Cite journal|last1=Tay|first1=W. C.|last2=Tan|first2=E. L.|last3=Heh|first3=D. Y.|date=2014|title=Fundamental Locally One-Dimensional Method for 3-D Thermal Simulation|journal=IEICE Transactions on Electronics|volume=E-97-C|issue=7|pages=636–644|doi=10.1587/transele.E97.C.636|bibcode=2014IEITE..97..636T|hdl=10220/20410 |hdl-access=free}}</ref><ref>{{Cite journal|last1=Heh|first1=D. Y.|last2=Tan|first2=E. L.|last3=Tay|first3=W. C.|date=2016|title=Fast Alternating Direction Implicit Method for Efficient Transient Thermal Simulation of Integrated Circuits|journal=International Journal of Numerical Modelling: Electronic Networks, Devices and Fields|volume=29|issue=1|pages=93–108|doi=10.1002/jnm.2049|hdl=10356/137201 |s2cid=61039449 |hdl-access=free}}</ref>
==Further reading==
*{{cite journal|accessdate=March 28, 2025
|url=https://www.researchgate.net/publication/265623760_50_Years_of_ADI_Methods_Celebrating_the_Contributions_of_Jim_Douglas_Don_Peaceman_and_Henry_Rachford |via=ResearchGate.net
|title=50 Years of ADI Methods: Celebrating the Contributions of Jim Douglas, Don Peaceman, and Henry Rachford
|first1=Adam |last1=Usadi |first2=Clint |last2=Dawson
|journal=SIAM News |volume=39|number=2|date=March 2006}} (Provides a review of the ADI methods and variants over the years.)</ref>
}}
== References ==
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