Euler and the improved euler methods Custom Essay
1. 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:
1 2 , 2 “(C) n < < n+ where x c x h y
2. Consider the initial value problem ‘ ( 1) , (0) 2. 2 y = x + y − y = 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.
