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This paper presents a numerical survey on electric field distribution in electrode arrangements commonly met while executing a live working on overhead lines. This numerical investigation is achieved using a software package based on charge simulating method. Particularly, the influence of the curvature of the bodies under stress on the maximal value of the electric field and the predominance between the axial and the radial components of the electric field are shown. This knowledge is of a great importance for accurately dimensioning the safety minimum approach distances (MAD) for future works to be performed with nonnormalised tools. First, a rod-plane-wall configuration is addressed and satisfactory results are obtained. This allows bringing up into general use of charge simulating program (CSP) to determine the safe MAD for complex configurations. A method that consists in use of the numerical techniques to adapt the empirical methods for the evaluation of the MAD, when tools of nonconventional dimensions are used, is then developed.

In the present work, we introduce the particle swarm optimization called (PSO in short) to avoid the Runge-s phenomenon occurring in many numerical problems. This new approach is tested with some numerical examples including the generalized integral quadrature method in order to solve the Volterra-s integral equations