One diffculty when using numerical techniques to solve for a systems evolution in time comes when the solution at a particular point in time depends on the previous time points, when there is some kind of memory in the system. Most often this memory effect is expressed in terms of differential equations, and their numerical approximation is often a signifcant source of error. This section will briefy review such approximations, focusing on those that are common in circuit analysis. With some exceptions, we will discuss what is known as initial value problems in numerical analysis We will start with the basic idea behind approximating continuous time/space differential equations and look at simple examples. This we follow with differential equations common in circuit analysis that arise from typical circuit elements.