Calculus/Euler's Method

Optimization Approximating Values of Functions 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 . 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 Examples A simple example is to solve the equation: This yields and hence, the updating rule is: Step size 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 is time. Optimization Approximating Values of Functions