Question

Consider the IVP -2.9y, (0) 2 for 0 sts1 The exact solution of this IVP is y-2e-291 The goal of this exercise is to visualize how Euler's method is related to the slope field of the differ ential equaton. In order to do this we will plot the direction field together with the approximations and the exact solution (c) Enter the function defining the ODE as anonymous. Use euler, with N = 5 to determine the approximation to the solution. Plot the approxi- mated points in red (use 'ro-, 'linewidth',2 as line-style in your plot), together with the exact solution and the direction field You should get Figure 2. The legend is not required, but to produce it, you can use legendC'Slope Field' 'Exact Sitn', 'Approx. Sltn (N-5)', 'location', 'northwest Based on the slope field and the geometrical meaning of Euler's method explain why the ap- proximations are so inaccurate for this particular value of the stepsize. Figure 2: Euler's method applied to2.9y, J(0)-2, N-5 compared to the exact solution

Answer why the approximations are so inaccurate for this particular value of the stepsize.

Answer 1

The approximations are so inaccurate for this particular value of the step size because where we take N=5 step size, we see larger variation and thus the error percentage increase. As we increase the step size, we obtain denser samples with smaller change in variation with the initial value problem and thus error reduces.

Hope this helps.