Time is continuous. Seconds, milliseconds or even microseconds are not the smallest unit of time, because it can be divided into infinite time points. Therefore, in simulation, it’s impossible for us to find a structure’s behavior at every single time point.What we can do is to solve the structure periodically with a designated time interval. How do we find an appropriate time interval and how do we relate the solutions at different time points? The answer is through time integration methods. In this course, we will discuss two main categories of time integration, implicit and explicit. We will learn about their features, differences, applications and how they work for flexible and rigid bodies in simulation.