SKEDSOFT

Then, we have the explicit method

...................1.8

The slope at the point x_{i 1}is replaced by an approximation to this slope. The method is called Heun’s method or Euler-Cauchy method.

Error of approximation:

The truncation error in the method is given by

where all the terms are evaluated at (x_i, y_i). Using the expressions for y′ and y″, we obtain

The truncation error is of order O(h3). Therefore, the method is of second order.