Exercises to Illustrate Runge-Kutta Methods

• Exercise 3.1 Derive the expansion (19) in the text.
• Exercse 3.2: Write out the system of equations (23) as in Example 11 for each of the following IVPs.
• Exercise 3.3: Approximate the solution to the following IVPs at t=0.3 using the Euler-Cauchy method with step size h=0.1.
• Exercise 3.4: A computer program to use the Euler, Euler-Cauchy and classical Runge-Kutta methods.
• Exercise 3.5: A computer program to use the classical Runge-Kutta method.
• Exercise 3.6: An analytical solution and Euler's Method.
• Exercise 3.7: Reduction of classical fourth order Runge-Kuta formula to Simpsons rule.