Abstract: The quasilinear differential equations are solved by finite difference method with non-equidistant scheme. The evolution of the runaway electron distribution function and wave energy density are obtained in interval of electron parallel velocity. These solutions are shown to be more complete than that given in [1] and [2] for both the stationary case and the evolution of functions in one-dimension. The results are useful for further study of runaways.

Key words: finite difference method, runaway electron, wave energy density