The thesis deals with the problem of calculating the potential distribution at a certain distance from a point impulse charge as well as from a point source of impulse current, which are described using the double-exponential approximation. The unknown parameters of the approximation function of the impulse function are estimated using the Marquardt method, which was created by upgrading the Gauss-Newton method. The second chapter describes the impulse point charge in the time and frequency domain, the double-exponential approximation, the transition from the frequency to the time domain using the inverse Fourier transform, and the analytical and numerical expression for the potential distribution at a selected distance from the impulse point charge, in the time domain. The third chapter describes the point source of impulse current, the double-exponential approximation of the impulse lightning current, the method of calculating the unknown parameters using the Marquardt method, and the numerical expression for the potential distribution at a selected distance from the impulse point source of current, in the time domain. The discrete inverse Fourier transform does not provide satisfactory results when calculating the potential distribution at greater distances from an impulse point charge. Therefore, a numerical algorithm based on the trapezoidal rule with a non-uniform distribution was developed, which provides results with a very high degree of accuracy. Comparisons of the analytical and numerical curves of the potential of a point impulse charge show that these two curves completely overlap for all selected distances from the source. The developed numerical algorithm was then applied to calculate the potential of a point source of an impulse current, in the time domain, for a selected set of distances from the source, where there is no analytical solution in the time domain. The purpose of the developed numerical algorithm is its application as a test algorithm during the development of advanced numerical algorithms for transient analysis of grounding systems.