13.2. Runge–Kutta Second-Order Method (RK2)

Try these first

1. 1.

   What is the formula for calculating k1 in RK2?

   Hint

   Remember, k1 is based on the initial values.

2. 2.

   In RK2, what does the second slope k2 represent?

   Hint

   Think about how we adjust for better accuracy.

3. 3.

   What is the order of accuracy for RK2?

   • First Order
   • Second Order
   • Third Order
   • Fourth Order

   Hint

   Think about how RK2 improves on simpler methods like Euler's.

4. 4.

   True or False: RK2 requires 4 function evaluations to update the solution.

   • True
   • False

   Hint

   Recall the steps involved in the RK2 process.

5. 5.

   Using the differential equation dy/dx = x^2 - y with the initial condition y(0) = 0 and step size h = 0.1, compute the value of y at x = 0.1 using RK2.

   Hint

   Remember to compute at both start and midpoint.

6. 6.

   Solve the initial value problem dy/dx = ln(x + 1) - y with y(0) = 1 and h = 0.1. Find y(0.1) using RK2.

   Hint

   Focus on the computation of k1 and k2 carefully.