Question

y’ – y = 2x -1 y(0) = 1 , 0 ≤ x ≤ 0.2   ...

y’ – y = 2x -1 y(0) = 1 , 0 ≤ x ≤ 0.2   

Use the Euler method to solve the following initial value problem

(a) Check whether the function y = 2 ex -2x- 1 is the analytical solution ;

(b) Find the errors by comparing the exact values you’re your numerical results (h = 0.05 and h = 0.1) and  Discuss the issue of numerical stability.

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
4. For the initial-value problem y′(t) = 3 + t − y(t), y(0) = 1: (i)...
4. For the initial-value problem y′(t) = 3 + t − y(t), y(0) = 1: (i) Find approximate values of the solution at t = 0.1, 0.2, 0.3, and 0.4 using the Euler method with h = 0.1. (ii) Repeat part (i) with h = 0.05. Compare the results with those found in (i). (iii) Find the exact solution y = y(t) and evaluate y(t) at t = 0.1, 0.2, 0.3, and 0.4. Compare these values with the results of...
Use Euler's method to approximate y(0.2), where y(x) is the solution of the initial-value problem y''...
Use Euler's method to approximate y(0.2), where y(x) is the solution of the initial-value problem y'' − 4y' + 4y = 0,  y(0) = −3,  y'(0) = 1. Use h = 0.1. Find the analytic solution of the problem, and compare the actual value of y(0.2) with y2. (Round your answers to four decimal places.) y(0.2) ≈     (Euler approximation) y(0.2) = -2.3869 (exact value) I'm looking for the Euler approximation number, thanks.
Consider the following differential equation: dydx=x+y With initial condition: y = 1 when x = 0...
Consider the following differential equation: dydx=x+y With initial condition: y = 1 when x = 0 Using the Euler forward method, solve this differential equation for the range x = 0 to x = 0.5 in increments (step) of 0.1 Check that the theoretical solution is y(x) = - x -1 , Find the error between the theoretical solution and the solution given by Euler method at x = 0.1 and x = 0.5 , correct to three decimal places
Consider the following initial value problems and solve by hand.              y' = 2x-3y+1              y(1)...
Consider the following initial value problems and solve by hand.              y' = 2x-3y+1              y(1) = 5 Let the step size 0.1. Then find the approximate value of y(1.2) by using Euler Method and Improved Euler Method. (Please show your work for both the Euler Method and the Improved Euler Method.)
6. Consider the initial value problem y' = ty^2 + y, y(0) = 0.25, with (exact)...
6. Consider the initial value problem y' = ty^2 + y, y(0) = 0.25, with (exact) solution y(t). (a) Verify that the solution of the initial value problem is y(t) = 1/(3e^(-t) − t + 1) and evaluate y(1) to at least four decimal places. (b) Use Euler’s method to approximate y(1), using a step size of h = 0.5, and evaluate the difference between y(1) and the Euler’s method approximation. (c) Use MATLAB to implement Euler’s method with each...
X/Y 1 2 3 4 -1 0 0 0.1 0.2 0 0.1 0.1 0 0.1 1...
X/Y 1 2 3 4 -1 0 0 0.1 0.2 0 0.1 0.1 0 0.1 1 0.2 0 0.1 0.1 let the joint probability mass function of the discrete random variable X and Y give as above Find E(3x+1) and E(3x+4y) cov( X,Y)
10.16: Write a user-defined MATLAB function that solves a first-order ODE by applying the midpoint method...
10.16: Write a user-defined MATLAB function that solves a first-order ODE by applying the midpoint method (use the form of second-order Runge-Kutta method, Eqs(10.65),(10.66)). For function name and arguments use [x,y]=odeMIDPOINT(ODE,a,b,h,yINI). The input argument ODE is a name for the function that calculates dy/dx. It is a dummy name for the function that is imported into odeMIDPOINT. The arguments a and b define the domain of the solution, h is step size; yINI is initial value. The output arguments, x...
The Duffing equation y'' + y + y 3 = 0 is a model for vibrations...
The Duffing equation y'' + y + y 3 = 0 is a model for vibrations of a mass attached to nonlinear spring. Use the vector Euler method with h = 0.2 to approximate the solution at t = 0.6 when the initial conditions are: y(0) = 0, y'(0) = 1.
Use Euler's method to approximate y(1.2), where y(x) is the solution of the initial-value problem x2y''...
Use Euler's method to approximate y(1.2), where y(x) is the solution of the initial-value problem x2y'' − 2xy' + 2y = 0,  y(1) = 9,  y'(1) = 9, where x > 0. Use h = 0.1. Find the analytic solution of the problem, and compare the actual value of y(1.2) with y2. (Round your answers to four decimal places.) y(1.2) ≈     (Euler approximation) y(1.2) =     (exact value)
Solve the IVP using the Eigenvalue method. x'=2x-3y+1 y'=x-2y+1 x(0)=0 y(0)=1 x'=2x-3y+1 y'=x-2y+1 x(0)=0 y(0)=1 Solve...
Solve the IVP using the Eigenvalue method. x'=2x-3y+1 y'=x-2y+1 x(0)=0 y(0)=1 x'=2x-3y+1 y'=x-2y+1 x(0)=0 y(0)=1 Solve the IVP using the Eigenvalue method. x'=2x-3y+1 y'=x-2y+1 x(0)=0 y(0)=1
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT