An eigenvalue problem with complex coefficient is consider in this paper. The mathematical model described the electrohydrodynamic instability of a layer of insulating liquid bounded by one side by rigid electrode and the other side is liquid-liquid interface and subjected to a electric field. Using th econtinuous analog of Newton's method, a numerical algorithm for solving this problem is developed. The original problem depend of many physical parameters for which the imaginary part of the eigenvalue with minimal absolute value vanish. It means that the oscillatory modes of instability can occur.
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