Question

Determine the numerical solution of the differential equation y'+y-x=0 using the Euler and the Runge-Kutta method...

Determine the numerical solution of the differential equation y'+y-x=0 using the Euler and the Runge-Kutta method until n = 5. The step size is 0.2, y(0) = 1.

No need to show calculations, I just need the summary of results of both methods with their percent absolute error from the exact value per yn.

Abs. error will be (Exact-Approx)/Exact * 100

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
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
Use C++ in Solving Ordinary Differential Equations using a Fourth-Order Runge-Kutta of Your Own Creation Assignment:...
Use C++ in Solving Ordinary Differential Equations using a Fourth-Order Runge-Kutta of Your Own Creation Assignment: Design and construct a computer program in C++ that will illustrate the use of a fourth-order explicit Runge-Kutta method of your own design. In other words, you will first have to solve the Runge-Kutta equations of condition for the coefficients of a fourth-order Runge-Kutta method.   See the Mathematica notebook on solving the equations for 4th order RK method.   That notebook can be found at...
Given (dy/dx)=(3x^3+6xy^2-x)/(2y) with y=0.707 at x= 0, h=0.1 obtain a solution by the fourth order Runge-Kutta...
Given (dy/dx)=(3x^3+6xy^2-x)/(2y) with y=0.707 at x= 0, h=0.1 obtain a solution by the fourth order Runge-Kutta method for a range x=0 to 0.5
x^2y'' − 3xy'+ 4y = 0 ; y(1)=5 y'(1)=3 differential equation using the Cauchy-Euler method
x^2y'' − 3xy'+ 4y = 0 ; y(1)=5 y'(1)=3 differential equation using the Cauchy-Euler method
x^2y'' − 3xy'+ 4y = 0 ; y(1)=5 y'(1)=3 differential equation using the Cauchy-Euler method
x^2y'' − 3xy'+ 4y = 0 ; y(1)=5 y'(1)=3 differential equation using the Cauchy-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.
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.
Find the general solution to the Cauchy-Euler equation: x^2 y'' - 5xy' + 8y = 0
Find the general solution to the Cauchy-Euler equation: x^2 y'' - 5xy' + 8y = 0
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...