Numerical instabilities hamper the computer simulation of axially symmetric, three-dimensional transient discharges from proceeding (Davies et al 1977).In the present paper, a method is presented in which suppression of the instabilities is attempted by avoiding numerical differentiation. The results when the present method is applied to simulation of a narrow, high-overvoltage discharge observed by Chalmers et al (1972) show that this method enables one to trace the cathode streamer reaching the cathode and the subsequent fronts propagating. The formation of the so-called radial constriction of the streamer is discussed.
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