A numerical method for approximating the values of a solution of a Differential Equation, by discretizing the differential equation into a difference equation that can be used to find the approximate solution through recursive definition. Similar methods include Heun’s Method and Runge-Kutta Method
where
Local Truncation Error:
Global Truncation Error:
Discrete Derivative
Example
This is the differential equation we are starting with.
Let be the time step between approximations. It will be in this example.
Use the initial condition to find
Equate the discrete derivative and the true derivative
We have a recursive definition of for arbitrary
Now let’s find the error at
Find the discrete
