The Mid Point Method

Let us look at the approximation of the previous section in more detail as it is applied to a single step of si ze . We get

with a step size of and

with two steps of size . Therefore,

The actual calculations involved are

(3.5)

Thus, the form of the method is similar to Euler's method in that the value at the end of the step is obtained by adding something to the value at the beginning of the step. It is called the mid-point method.

Note: It is easy to verify the local truncation error of (3.5) is .