7. Interpolation & Numerical Methods

Try these first

1. 1.

   What does IVP stand for?

   Hint

   Think about what is 'initial' in the context of ODEs.

2. 2.

   What is the formula for Euler’s Method?

   Hint

   Remember, it involves a step size and a slope.

3. 3.

   Which method is simplest for solving ODEs?

   • Euler’s Method
   • Runge-Kutta
   • Taylor Series

   Hint

   Consider the method that involves basic slope approximation.

4. 4.

   True or False: RK4 is less accurate than Euler's Method.

   • True
   • False

   Hint

   Think about why we would use RK4 over Euler's.

5. 5.

   Using Euler's Method, approximate y(1) for dy/dx = 2x + y, with y(0) = 1 and step sizes of 0.1.

   Hint

   Profit from your known initial condition to steer each step correctly.

6. 6.

   Using the Simpson’s Rule within a Predictor-Corrector scheme, find an approximation for y(0.5) given dy/dx = -2y with y(0) = 1.

   Hint

   Use RK4 to get your starting values for correction.