Use Euler's method with each of the following step sizes to estimate the value of y(0.8),...

Use Euler's method with each of the following step sizes to estimate the value of y(0.8), where y is the solution of the initial-value problem: y' = y, y(0) = 5.

(i) h = 0.8

y(0.8) = 9

(ii) h = 0.4

y(0.8) = 9.8

(iii)

h = 0.2

y(0.8) = ?

The error in Euler's method is the difference between the exact value and the approximate value. Find the errors made in part (a) in using Euler's method to estimate the true value of y(0.8), namely 5e^0.8.

(Round your answers to four decimal places.)

h = 0.8	error = (exact value) − (approximate value) = 2.1277
h = 0.4	error = (exact value) − (approximate value) = 1.3277
h = 0.2	error = (exact value) − (approximate value) = ?

Expert Solution

milcah answered 2 years ago

Exercise (a) Use Euler's method with each of the following step sizes to estimate the value...

Exercise (a) Use Euler's method with each of the following step sizes to estimate the value of y(1.6), where y is the solution of the initial-value problem y' = y, y(0) = 6. (i) h = 1.6 (ii) h = 0.8 (iii) h = 0.4 Exercise (b) We know that the exact solution of the initial-value problem in part (a) is y = 6ex. Draw, as accurately as you can, the graph of y = 6ex, 0 ≤ x ≤ 1.6, together with...

Use Euler's method with step size 0.2 to estimate y(0.4), where y(x) is the solution of the...

Use Euler's method with step size 0.2 to estimate y(0.4), where y(x) is the solution of the initial-value problem y' = 3x − 4xy, y(0) = 0. (Round your answer to four decimal places.) y(0.4) = (b) Repeat part (a) with step size 0.1. (Round your answer to four decimal places.) y(0.4) =

Use Euler's method with the given step size to estimate y(1.4) where y(x) is the solution...

Use Euler's method with the given step size to estimate y(1.4) where y(x) is the solution of the initial-value problem y′=x−xy ,y(1)=3.

Use Euler's Method with step size 0.11 to approximate y (0.55) for the solution of the...

Use Euler's Method with step size 0.11 to approximate y (0.55) for the solution of the initial value problem y ′ = x − y, and y (0)= 1.2 What is y (0.55)? (Keep four decimal places.)

Use Euler's method with step size 0.5 to compute the approximate y-values y1, y2, y3 and...

Use Euler's method with step size 0.5 to compute the approximate y-values y1, y2, y3 and y4 of the solution of the initial-value problem. y' = y − 5x, y(3) = 1. y1 = ______ y2 =______ y3 =_______ y4=________ Please show all work, neatly, line by line and justify steps so that I can learn. Thank you!

1. Use Euler's method with step size 0.50.5 to compute the approximate yy-values y1≈y(0.5), y2≈y(1),y3≈y(1.5), and...

1. Use Euler's method with step size 0.50.5 to compute the approximate yy-values y1≈y(0.5), y2≈y(1),y3≈y(1.5), and y4≈y(2) of the solution of the initial-value problem y′=1+3x−2y, y(0)=2. y1= y2= y3= y4= 2. Consider the differential equation dy/dx=6x, with initial condition y(0)=3 A. Use Euler's method with two steps to estimate y when x=1: y(1)≈ (Be sure not to round your calculations at each step!) Now use four steps: y(1)≈ B. What is the solution to this differential equation (with the given initial...

Consider the initial value problem given below. y'=x+4cos(xy), Y(0)=0 Use the improved Euler's method subroutine with...

Consider the initial value problem given below. y'=x+4cos(xy), Y(0)=0 Use the improved Euler's method subroutine with step size h=0.3 to approximate the solution to the initial value problem at points x= 0.0,0.3,0.6.....3.0

Use the Runge-Kutta method and the Runge-Kutta semilinear method with the indicated step sizes to ﬁnd...

Use the Runge-Kutta method and the Runge-Kutta semilinear method with the indicated step sizes to ﬁnd approximate values of the solution of the given initial value problem at 11 equally spaced points (including the endpoints) in the interval. This question is from the differential equation. y'-4y = x/y^2(y+1) , y(0) = 1; h=0.1, 0.05 , 0.025, on [0, 1]

Let y′=y(4−ty) and y(0)=0.85. Use Euler's method to find approximate values of the solution of the...

Let y′=y(4−ty) and y(0)=0.85. Use Euler's method to find approximate values of the solution of the given initial value problem at t=0.5,1,1.5,2,2.5, and 3 with h=0.05. Carry out all calculations exactly and round the final answers to six decimal places.

Use the improved Euler's method to obtain a four-decimal approximation of the indicated value. First use...

Use the improved Euler's method to obtain a four-decimal approximation of the indicated value. First use h = 0.1 and then use h = 0.05. y' = y − y^2, y(0) = 0.8; y(0.5) y(0.5) ≈________ (h = 0.1) y(0.5) ≈ _________(h = 0.05)

Question