This paper reformulates the non-linear differential equations associated with time varying resistance in minimal cardio-vascular system models into a system of linear equations with an analytical solution. The importance of including time varying resistance is shown for a single chamber model where there is a 17.5% difference in cardiac output when compared with a constant resistance model. However, the increased complexity has significant extra computational cost. This new formulation provides a significant computational saving of 15x over the previous method. This improvement enables more physiological accuracy with minimal cost in computational time. As a result, the model can be used in clinical situations to aid diagnosis and therapy selection without compromising on physiological accuracy.