Assignment:
Q1. Consider the initial value problem y' = 2xy, y(1) = 1. Use the Euler's method and improved Euler's method with h = 0.1and h = 0.05 to obtain approximate values of the solution at x = 1.5. At each step compare the approximate value with the actual value of the analytic solution. Also calculate the bound for the local truncation error using the formula:
Q2. Consider the initial value problem
Use the improved Euler's method with h = 0.1and h = 0.05 to obtain approximate values of the solution at x = 0.5. At each step compare the approximate value with the actual value of the analytic solution.
Provide complete and step by step solution for the question and show calculations and use formulas.