The total flow of the optimal isotope separation cascade should be kept at a minimum to ensure economic viability. The concept of virtual components has proven useful in optimizing and designing cascades for multi-component isotope separation, but is only used in cases with an available analytical solution. Practical situations are complicated and resort to numerical simulations because there are no analytical solutions. Therefore, a generalization for numerical methods is required. A major difficulty in generalization is that mass conservation requires the concentration of a virtual component to be zero, which causes numerical problems. This paper proposes an approach to overcome this difficulty and develops a numerical method accordingly. The matched-R cascade is used as an example for numerical experiments to show that a cascade is solely determined by the choice of the two virtual components, and to demonstrate how the numerical method is applied to find the optimal cascade. (C) 2014 Elsevier Ltd. All rights reserved.