14.4. Example Problem

Try these first

1. 1.

   What is the initial condition given in the example problem?

   Hint

   Check the initial value provided in the problem statement.

2. 2.

   What is the step size used in the calculations?

   Hint

   Look for the step size mentioned in the problem.

3. 3.

   What is the final value of y(0.4) as calculated in the example?

   • 1.4832
   • 1.5836
   • 1.7421

   Hint

   Remember the result from the example problem.

4. 4.

   True or False: The Predictor-Corrector method uses only one step to solve ODEs.

   • True
   • False

   Hint

   Consider the methodology of the Milne's method.

5. 5.

   Using the Milne method, determine y(0.5) given new initial conditions: y(0) = 1, y(0.1) = 1.1, y(0.2) = 1.21, y(0.3) = 1.331 as well as the step size h = 0.1. Show all work.

   Hint

   Stay consistent with your notation and ensure all previous y and f values are correct before proceeding.

6. 6.

   If f(x,y) = 2y + x and y(0) = 2. Using Milne's method, solve for y(0.1) and determine how the solution would differ if the initial value was y(0) = 1 instead.

   Hint

   Focus on the significance of initial conditions in numerical methods.