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HandWiki. Alternating Direction Implicit Method. Encyclopedia. Available online: https://encyclopedia.pub/entry/29284 (accessed on 11 October 2026).
HandWiki. Alternating Direction Implicit Method. Encyclopedia. Available at: https://encyclopedia.pub/entry/29284. Accessed October 11, 2026.
HandWiki. "Alternating Direction Implicit Method" Encyclopedia, https://encyclopedia.pub/entry/29284 (accessed October 11, 2026).
HandWiki. (2022, October 14). Alternating Direction Implicit Method. In Encyclopedia. https://encyclopedia.pub/entry/29284
HandWiki. "Alternating Direction Implicit Method." Encyclopedia. Web. 14 October, 2022.
Alternating Direction Implicit Method
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In numerical linear algebra, the Alternating Direction Implicit (ADI) method is an iterative method used to solve Sylvester matrix equations. It is a popular method for solving the large matrix equations that arise in systems theory and control, and can be formulated to construct solutions in a memory-efficient, factored form. It is also used to numerically solve parabolic and elliptic partial differential equations, and is a classic method used for modeling heat conduction and solving the diffusion equation in two or more dimensions. It is an example of an operator splitting method.

operator splitting numerically diffusion equation

References

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  2. Lu, An; Wachspress, E.L. (1991). "Solution of Lyapunov equations by alternating direction implicit iteration". Computers & Mathematics with Applications 21 (9): 43–58. doi:10.1016/0898-1221(91)90124-m. ISSN 0898-1221.  https://dx.doi.org/10.1016%2F0898-1221%2891%2990124-m
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  26. Gan, T. H.; Tan, E. L. (2013). "Unconditionally Stable Fundamental LOD-FDTD Method with Second-Order Temporal Accuracy and Complying Divergence". IEEE Transactions on Antennas and Propagation 61 (5): 2630–2638. doi:10.1109/TAP.2013.2242036. https://www.ntu.edu.sg/home/eeltan/papers/2013%20Unconditionally%20Stable%20Fundamental%20LOD-FDTD%20Method%20With%20Second-Order%20Temporal%20Accuracy%20and%20Complying%20Divergence.pdf. 
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  28. Heh, D. Y.; Tan, E. L.; Tay, W. C. (2016). "Fast Alternating Direction Implicit Method for Efficient Transient Thermal Simulation of Integrated Circuits". International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 29 (1): 93–108. doi:10.1002/jnm.2049.  https://dx.doi.org/10.1002%2Fjnm.2049
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