14.. Numerical Solutions of ODEs

Try these first

1. 1.

   Define the term 'Ordinary Differential Equation'.

   Hint

   Think about what the term 'ordinary' implies compared to other types of differential equations.

2. 2.

   What is the primary function of the Predictor Formula?

   Hint

   What does 'predict' suggest?

3. 3.

   What is the purpose of the Predictor Formula in Milne's method?

   • To compute function values
   • To estimate future values
   • To find the exact solution

   Hint

   What does 'predict' relate to in terms of future values?

4. 4.

   True or False: The Corrector Formula is an explicit method.

   • True
   • False

   Hint

   Recall how the Corrector refines the estimates.

5. 5.

   Given the ODE dy/dx = 2x + 3y, compute the values for y(0.1) up to y(0.5) using Milne's method with h=0.1 after obtaining initial values from another method.

   Hint

   Ensure to derive initial values using a reliable method before applying Milne’s calculation.

6. 6.

   Critique the effectiveness of Milne’s method compared to a Runge-Kutta method in solving stiff equations.

   Hint

   What makes one method better suited for stiff equations than the other?