This thesis aims to develop a MATLAB code capable of performing a fast transient analysis of a microprocessor's power delivery network (PDN). The initial phase of the research involved implementing the Waveform Relaxation (WR) method, also known as the perturbation approach, to simulate power integrity. The WR method showed promising results when applied to simpler PDNs, successfully validating signal behavior under transient conditions. However, in more complex PDN configurations, the method revealed significant convergence issues, tending towards numerical instability and divergence. To overcome these limitations, the research shifted to the Picard iteration method. This approach, similar to WR, calculates solutions iteratively, improving convergence by summing the computed error at each iteration step until reaching a predetermined accuracy.