Euler's Method - dy/dt = y^2-4t

In summary, the conversation discusses using Euler's method to make a table for the given equation and initial conditions. The formula for Euler's method is provided and it is clarified that the t variable should be substituted in for t and the y variable for y. The first line of the table is also provided as an example.
  • #1
killersanta
63
0

Homework Statement



dy/dt = y^2-4t - y(0) = 0.5 - 0 <_ t <_ 3.0 - Change in t = 0.5

I have to use Euler's method to make a table, but I'm not sure how to handle the t. I have only done it with y's and no other variables.
 
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  • #2
Eulers method is given as:

[tex]
y_{i+1}=y_{i}+hy'(t_{i},y_{i})
[/tex]

So in your case the equation would be:

[tex]
y_{i+1}=y_{i}+h(y_{i}^{2}-4t_{i})
[/tex]

Understand now?
 
  • #3
I think, I just started putting the t's in for t and the y's for y... So for the first line I got:
K: 0
t:0
y:0.5
dy/dt(t,y) = .25
Change in t*dy/dt(t,y) = .125
 
  • #4
Looks okay to me.
 
  • #5
Sweet, Thanks.
 

1. What is Euler's Method?

Euler's Method is a numerical approach for approximating the solution to a first-order differential equation. It involves breaking down the continuous function into smaller intervals and using linear approximations to estimate the solution at each interval.

2. What is the equation used in Euler's Method?

The equation used in Euler's Method is dy/dt = f(t,y), where t represents the independent variable, y represents the dependent variable, and f(t,y) is the differential equation to be solved.

3. How do you use Euler's Method to solve a differential equation?

To use Euler's Method, you first need to determine the initial condition for the differential equation, which is the value of y at t=0. Then, you divide the interval of t into smaller intervals, and use the following formula to approximate the solution at each interval: yn+1 = yn + f(tn, yn) * Δt. Repeat this process until you reach the desired value of t.

4. What is the purpose of using Euler's Method?

Euler's Method is used when it is not possible to find the exact solution to a differential equation. It provides a close approximation to the solution and can be used to solve a wide range of differential equations.

5. What are the limitations of Euler's Method?

Euler's Method is a first-order approximation and can introduce errors in the solution, especially for large intervals or when the function has large changes. It also does not guarantee the convergence of the solution and can give inaccurate results for certain types of differential equations.

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