Question

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.

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

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.
Given the second-order differential equation y''(x) − xy'(x) + x^2 y(x) = 0 with initial conditions...
Given the second-order differential equation y''(x) − xy'(x) + x^2 y(x) = 0 with initial conditions y(0) = 0, y'(0) = 1. (a) Write this equation as a system of 2 first order differential equations. (b) Approximate its solution by using the forward Euler method.
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.
The differential equation given as dy / dx = y(x^3) - 1.4y, y (0) = 1...
The differential equation given as dy / dx = y(x^3) - 1.4y, y (0) = 1 is calculated by taking the current h = 0.2 at the point x = 0.6 and calculated by the Runge-Kutta method from the 4th degree, find the relative error. analytical solution: y(x)=e^(0.25(x^4)-1.4x)
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 problem: dy/dt = -3 - 2 * t2,       y(0) = 2...
Consider the following initial value problem: dy/dt = -3 - 2 * t2,       y(0) = 2 With the use of Euler's method, we would like to find an approximate solution with the step size h = 0.05 . What is the approximation of y (0.2)?  
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...
Solve the initial value problem below for the Cauchy-Euler equation t^2y"(t)+10ty'(t)+20y(t)=0, y(1)=0, y'(1)=2 y(t)=
Solve the initial value problem below for the Cauchy-Euler equation t^2y"(t)+10ty'(t)+20y(t)=0, y(1)=0, y'(1)=2 y(t)=
a) Let y be the solution of the equation y ′ − [(3x^2*y)/(1+x^3)]=1+x^3 satisfying the condition  y...
a) Let y be the solution of the equation y ′ − [(3x^2*y)/(1+x^3)]=1+x^3 satisfying the condition  y ( 0 ) = 1. Find y ( 1 ). b) Let y be the solution of the equation y ′ = 4 − 2 x y satisfying the condition y ( 0 ) = 0. Use Euler's method with the horizontal step size  h = 1/2 to find an approximation to the value of the function y at x = 1. c) Let y...