Stability function for a basic RK method

[dynamicskillingme]

Homework Statement

Hi, can someone explain how they get this stability function.

Homework Equations

http://blob:http://imgur.com/840ee1fe-f09c-49ab-bdbb-7f953777f900

The Attempt at a Solution

I have attempted to do it two ways, and I'm not sure if I'm just having an awfully bad day at maths or am doing it wrong.

I have tried putting in

but the answer has been coming out wrong, so a worked solution to work out what I've been doing wrong would be great

 

[mighty2000]

Hi there, I can help you with understanding the stability function. The stability function is a mathematical representation of the stability of a system. It is used to determine whether a system is stable or unstable, based on its transfer function. In order to calculate the stability function, we need to follow a few steps:

1. Write the transfer function in the form of (s+a)/(s+b), where a and b are constants.
2. Take the absolute value of the transfer function, |(s+a)/(s+b)|, and set it equal to 1.
3. Solve for s to determine the values of s that make the absolute value equal to 1.
4. Plot these values on the complex plane.
5. If all the values lie on the left half of the plane, the system is stable. If any values lie on the right half, the system is unstable.

For the transfer function given in your post, we can write it as (s+1)/(s+2). Taking the absolute value and setting it equal to 1, we get |(s+1)/(s+2)|=1. Solving for s, we get s=-1 or s=-2. Plotting these values on the complex plane, we see that both values lie on the left half of the plane, indicating that the system is stable.

I'm not sure where you went wrong in your attempts, but I hope this explanation helps you understand the process better. Let me know if you have any further questions.