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Abstract
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To investigate the effects of different anchoring conditions of the nematic molecules at the walls on the Frederiks transition, we have used finite difference method to solve the Euler–Lagrange equation of the ferronematic total free energy provided by [1,2]. In order to deal with these difficult boundary conditions, we have used finite difference method together with the relaxation method to present the periodic solutions of the nematic director orientations at the interfaces. Then, in the interval from zero to half-π, Maxwell construction method is employed to select a physical solution for nematic director at the interfaces of a slab. In this way, NLC director rotates toward the normal to the surface as the applied electric field increases at the walls. Meaning, the solution reaches from 0 to π/2 as the electric field increases
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