Ground Potential Rise (GPR) is an important factor for a grounding system that must be properly designed to protect people against any dangerous induced voltages and to avoid damages in equipment. In this context, several approaches to assess GPR are available in the literature which can be developed either directly in time domain or frequency-to-time transforms. The purpose of this paper is to investigate the performance of two time-domain recursive methods to compute the transient GPR in grounding systems generated by different lightning currents. First, the grounding impedances are calculated by a full-wave electromagnetic software FEKO with numerical Method of Moments from 100 Hz to 5 MHz. The GPRs are assessed by a recursive convolution method (M1) and by a recursive trapezoidal integration method (M2). Both methods employ the Vector Fitting technique on each impedance curve adjusted into a poles-residues form. Then, simulation results from the recursive methods are compared with those obtained with frequency-to-time method using the Numerical Laplace Transform (NLT) and with the equivalent circuit incorporated in the ATP-software. Results show a good agreement between the responses from recursive methods in comparison with those from NLT and ATP-software. As advantages, the recursive methods are an alternative tool when no analytical expressions for lightning currents are known or only measured data is provided. Additionally, the circuit implementation in Electromagnetic Transient (EMT)-type software tools is not needed to compute the transient GPRs in time domain. This work is an extension of a 2019-SIPDA conference paper [1].