These extra practice problems are for students who wish to have an extra set to practice. These problems do not have a posted solution so students should reflect on ways to determine whether their answer is correct. Feel free to discuss with peers to solve these problems.
Solve the following equation using Euler’s method when x = 0, and y = 3 until x = 5. Use step sizes of h = 1, 0.5, 0.25, and 0.1 and compare the answers in a graph.
Solve the following equation using Euler’s, Heun’s, Midpoint, and Ralston’s method when x = 0, and y = 10 until x = 5 and h = 1. Compare the answers in a graph.
Solve the following ODE using Euler’s method and RK4 when x= 1, y =1, and h = 0.5. Continue until x = 10.
Use Ralston’s method to solve from x = 0 to x = 2. When x = 0, y1 = 1, and y2 = 2. Choose an appropriate step size.