Differential Equations-Eulers Method

In summary, Euler's Method is a numerical method used to approximate the solution of first-order differential equations. It is commonly used in fields such as physics and engineering when an analytical solution is not practical. The method works by approximating the solution at discrete points using small steps, and its advantages include its simplicity and accessibility. However, a limitation is that it can only provide an approximation and the size of the step can affect its accuracy.
  • #1
jawhnay
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Homework Statement


[URL=http://imageshack.us/photo/my-images/860/64863644.png/][IMG=http://img860.imageshack.us/img860/4563/64863644.png][/URL] Uploaded with ImageShack.us[/PLAIN]

Homework Equations

The Attempt at a Solution


I'm having trouble setting up the equation. This is how I set it up, but I'm not sure if it's correct.
T(1)= 100 + 0.1(1)(70-100)

Sorry about the link. It was kind of long and I needed an answer fast so I didn't want to waste time typing the question.
 
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  • #2
Thats definitely the basic idea. What are the units of 'h' ? (How is 'h' defined?)
 

What is Euler's Method?

Euler's Method is a numerical method used to approximate the solution of a first-order differential equation. It is a simple and straightforward algorithm that uses small steps to approximate the solution.

When is Euler's Method used?

Euler's Method is typically used when the differential equation cannot be solved analytically, or when the analytical solution is too complex to be practical. It is commonly used in physics, engineering, and other fields that involve modeling real-world systems.

How does Euler's Method work?

Euler's Method works by approximating the solution of a differential equation at discrete points. It starts with an initial condition, and then uses a series of small steps (calculated using the derivative of the function at each point) to estimate the value of the function at the next point. This process is repeated until the desired level of accuracy is reached.

What are the advantages of using Euler's Method?

Euler's Method is a relatively simple and easy-to-understand algorithm, making it a popular choice for approximating solutions to differential equations. It also does not require advanced mathematical knowledge, making it accessible to a wide range of users.

What are the limitations of Euler's Method?

One limitation of Euler's Method is that it can only approximate the solution to a differential equation, and therefore may not always be accurate. Additionally, the size of the step used in the algorithm can affect the accuracy of the approximation. Using too large of a step can result in a significant error in the estimated solution.

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