A new iterative method for calculating the distribution of a liquid-crystal director is presented, which is based on a straightforward finite-difference approximation to the Euler-Lagrange equations. The method is applicable for various types of liquid-crystal displays, such as the twist nematic cell, nematic cell with asymmetic pretilt, or chiral supertwist nematic cell. This method is very stable and simple, and can give accurate results in a short time compared with Newton's method, the relaxation method, simulated annealing, etc.
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