The complexity of operational conditions in stable isotope separation cascades necessitates the utilization of numerical methods for cascade design and performance analysis. This study focuses on solving a system of nonlinear algebraic equations derived from the mass and energy balance equations, which is a fundamental challenge in analyzing and designing cascades and developing numerical methods. Two existing numerical algorithms were selected from the literature and modified for quasi-ideal cascade systems. The performance of these algorithms was examined and compared, with a particular emphasis on influential parameters such as the number of stages, the number of isotopes, and the separation factor. The first algorithm solves the concentration and flow equations separately, while the second algorithm solves all equations simultaneously. The results indicate that the first algorithm exhibits significant superiority over the second algorithm. In most cases, the second algorithm either fails to converge or exhibits a slower convergence speed. Additionally, the results demonstrate that increasing the number of stages impacts the convergence time, while an increase in the separation factor leads to greater convergence complexity.