Module 2: Single Step Methods
  Lecture 4: The Euler Method
 

 

  1. We finally may assume the possibility of expanding the solution in a Taylor series around the point

    Truncating the series after the linear term in yields the Euler's method.

    2. Remark: Each of these interpretations points the way to a class of generalizations of Euler's method and it is interesting to note that the generalization indicated by (i) (numerical differentiation), which seems to be the most straight forward, has proved to be the least fruitful of the three.