dcash/dt = income What this says mathematically is that the change in cash with time is equivalent to the income on the account. Let us look at another simple example from the STELLA documentation. Imagine we are dealing with a cooling cup of coffee. A STELLA model of this system might look like: The heat flow (labeled cooling) from the coffee to the surrounding air is driven by the difference in temperature between the two. When the coffee is very hot, the flow of heat is relatively high (unless you are drinking your coffee in a sauna). When the coffee is cooler, the flow of heat is smaller. Therefore, the temperature vs. time curve looks like a negative exponential function, and the curve is completely continuous in time: Here is the analytical equation that describes the cooling: This equation says that the change in temperature with time (dT/dt) is a function of the temperature (T; a is a constant of proportionality that reflects the temperature difference between the coffee and the ambient air). After a bit of calculus, the solution to this equation is: In the case of the figure above, T0 = 100 °C and a = 0.5. In simulating the cooling of a cup of coffee, the computer is unable to replicate this continuous curve. Instead, it must calculate what the temperature is at discrete time intervals and then use these temperature-time points to approximate the cooling curve. The first step in this approximation is for the computer to divide the total simulation time by the time step length to determine how many times it will have to carry out its calculations. Next, the software creates a list of all of the equations it is going to have to use (input by the user) and the order in which they are to be executed. It then takes the initial conditions of the model and uses them to estimate the change in the stocks (the reservoir contents) and flows over the first time step. The changes in the stocks and flows are added to the initial values to determine the new values at the first time step.
dcash/dt = income What this says mathematically is that the change in cash with time is equivalent to the income on the account. Let us look at another simple example from the STELLA documentation. Imagine we are dealing with a cooling cup of coffee. A STELLA model of this system might look like: The heat flow (labeled cooling) from the coffee to the surrounding air is driven by the difference in temperature between the two. When the coffee is very hot, the flow of heat is relatively high (unless you are drinking your coffee in a sauna). When the coffee is cooler, the flow of heat is smaller. Therefore, the temperature vs. time curve looks like a negative exponential function, and the curve is completely continuous in time: Here is the analytical equation that describes the cooling: This equation says that the change in temperature with time (dT/dt) is a function of the temperature (T; a is a constant of proportionality that reflects the temperature difference between the coffee and the ambient air). After a bit of calculus, the solution to this equation is: In the case of the figure above, T0 = 100 °C and a = 0.5. In simulating the cooling of a cup of coffee, the computer is unable to replicate this continuous curve. Instead, it must calculate what the temperature is at discrete time intervals and then use these temperature-time points to approximate the cooling curve. The first step in this approximation is for the computer to divide the total simulation time by the time step length to determine how many times it will have to carry out its calculations. Next, the software creates a list of all of the equations it is going to have to use (input by the user) and the order in which they are to be executed. It then takes the initial conditions of the model and uses them to estimate the change in the stocks (the reservoir contents) and flows over the first time step. The changes in the stocks and flows are added to the initial values to determine the new values at the first time step.
student_exercise_unit_1.v5.docx