Question

a use Euler's method with each of the following step sizes to estimate the value of y 0.4 where y is the solution of the initial value problem y -y, y 0 3 カー0.4 0.4) (i) y10.4) (in) h= 0.1 b we know that the exact solution of the initial value problem n part a s yー3e ra , as accurately as you can the graph of y e r 4 together with the Euler approximations using the step sizes npa tak our etches should resemble the figures ror the irst Euler approximation, Euler approximation with step size 0.S, and Euler appraximation with step size 0.25.) Use your sketches to decide whether your estimates ipart (a) are underestimates or The estimates areSelect (c)The error in Euler's methad is the difference between the exact value and the approximate value. Find the erros mde in part (a) in using Euler's method to estimate the true value of yto.4), namely, 30.4, (Round your answers to four decimal places.) h 0.4 er-(exact value) - (approximate value) h 0.2 errr (exact value) (approximate value) h-0.1 error - (exact value) - (approximate value) - What happens to the error each time the step size is halved? Each time the step size is halved, the error estimate appears to be (approximately)

Answer 1

d에 Ctin) 4.39 23 y(0.4) Cu) 0 exact34 47S Ееасト 3 3-664 Ts Culev 3 2

| 3.3,Sr | 3.6642 | 4.oy% | 4.4.1 S5 Culess 3 3.3 3-63 3993 392 hon 4キ h=0.2- heo ev enim h-o 2wor =44755-43923 = o.. o f32