Exercise 4 The Exact Solution To Y X Y Y 0 2 Is Y X 1 3e 2 It S A Linear Equation Use Your Spreadsheet 1 (60.15 KiB) Viewed 35 times
Exercise 4 The exact solution to y' = x - y, y(0) = 2 is y = x – 1+ 3e-2. (It's a linear equation.) Use your spreadsheet to complete the following table. The first column indicates the step size, the second column shows the approximation of y(2) using the improved Euler method, and the last column shows the relative error in the approximation. (Record 4 significant digits for the second and third columns.) h y(2) approx. rel. error 0.1 1.407 0.1039% 0.05 0.025 0.006131% 0.0125 1.406
Exercise 5 = Imagine that you used Euler's method and improved Euler's method to approximate y(4), where y is the solution of an initial value problem y' = f(x,y), y(0) = a, and then reported the relative errors in the two approximations for different step sizes. Use what you know about the two methods to make your best guesses for the missing table values below. (Record 4 significant digits.) h rel. error Euler rel. error improved Euler 0.1 0.05 10.99% 9.330% 0.025 0.0125
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