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=== Relations to other implicit methods ===
Many classical implicit methods by Peachman-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|via=}}</ref><ref>{{Cite journal|last=Gan|first=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|via=}}</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|last=Tay|first=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|url=|journal=IEICE Transactions on Electronics|volume=E-97-C|issue=7|pages=636-644|doi=10.1587/transele.E97.C.636|via=}}</ref><ref>{{Cite journal|last=Heh|first=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|url=|journal=International Journal of Numerical Modelling: Electronic Networks, Devices and Fields|volume=29|issue=1|pages=93-108|doi=10.1002/jnm.2049|via=}}</ref>
== References ==
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