![]() ![]() ![]() Well, with these methods, we assume that we are looking for a position in some space, usually denoted as, but we can use any variable. Now, how does this relate to the Euler methods? This equation allows us to find the position of an object based on it's previous position (), the derivative of it's position with respect to time () and one derivative on top of that ().Īs stated in the Tayor Series Expansion, the acceleration term must also have in front of it. Where is position, is velocity, and is acceleration. So, what does this mean? Well, as mentioned, we can think of this similarly to the kinematic equation: Like before, is some function along real or complex space, is the point that we are expanding from, and denotes the derivative of. These expansions basically approximate functions based on their derivatives, like so: In this case, it makes sense for me to see Euler methods as extensions of the Taylor Series Expansion. They introduce a new set of methods called the Runge Kutta methods, which will be discussed in the near future!Īs a physicist, I tend to understand things through methods that I have learned before. ![]() The Euler methods are some of the simplest methods to solve ordinary differential equations numerically. ![]()
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