Hi. My first post! I am trying to complete this exercise:
- Although it might not be obvious from the differential equation, its solution could “behave badly” near a point x at which we wish to approximate y(x). Numerical procedures may give widely differing results near this point. Let y(x) be the solution of the initial-value problem y' = x^2 + y^3, y(1) = 1. (a) Use a numerical solver to graph the solution on the interval [1, 1.4]. (b) Using the step size h = 0.1, compare the results obtained from Euler’s method with the results from the improved Euler’s method in the approximation of y(1.4). Please help? THANK YOU!
