Euler's Method is a method for estimating the value of a function based upon the values of that function's first derivative.
The general algorithm for finding a value of is:
where f is y'(x). In other words, the new value, , is the sum of the old value and the step size times the change, .
You can think of the algorithm as a person traveling with a map: Now I am standing here and based on these surroundings I go that way 1 km. Then, I check the map again and determine my direction again and go 1 km that way. I repeat this until I have finished my trip.
The Euler method is mostly used to solve differential equations of the form
A simple example is to solve the equation:
This yields and hence, the updating rule is:
Step size = 0.1 is used here.
The easiest way to keep track of the successive values generated by the algorithm is to draw a table with columns for .
The above equation can be e.g. a population model, where y is the population size and x a decease that is reducing the population.