The effect of a numerical grid on the solution obtained by the particle-in-cell method is considered. It is shown that the solution essentially depends on the form of a model particle (kernel). Several kernels including those with four and three nodes are analytically and numerically analyzed in the one-dimensional case. Some numerical results obtained for the one-dimensional problem of breakdown of a discontinuity in a dispersion medium are discussed. A new modification of the form-factor with a decreased self-force is proposed. This work was supported by the Novosibirsk Technical State University (project RNP.2.2.1.1.3653).

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