Sorry if I wasn't clear enough, I don't understand the concept behind the generating polynomials. My notes state the examples of the three theta methods but I can't understand how they are obtained (e.g. implicit euler is sigma(w) = w )
Hi, I'm struggling to understand how the generating polynomials work and are implemented in the difference equation for a general ODE y' = f(t,y)
Difference Equation
Generating polynomials
"Coefficients are normalized either by a_k = 1 or sigma(1) = 1
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...
If you could humour me as an engineer having to take a maths course and is struggling to remember concepts taught along time ago, How could I prove their answer, or what should I read up on to be able to show this proof?
Homework Statement
Has solution
It then goes on to state the solution blows up at , which I understand.
My issue is when I do the solution I get
(Working)
My Hamilton was a mess from a mistake early on. After redoing it I get .
I can then formulate the hamiltonian jacobi again and get
Then (and I'm mostly going from an example in my lecture notes and the question hints) I can separate the variables out as
That can be substituted as
In...
Homework Statement
Homework EquationsThe Attempt at a Solution
So far I have a solution for a) as
For b) I formulate the equation as
and so far for c) I have
My main idea at the moment is that as the Lagrangian was not time dependent, the Hamiltonian will not be. Following on maybe...
Homework Statement
Hi, I'm working on understanding how a time independent point transformation . effects the Lagrangian and to see how what values are co and contra variant.Homework Equations
Would these be correct formulations, or have I overlooked something?
The Attempt at a Solution
and...
Its a mechanical system, but just working on proofs and theory so
I'm working on proving how different quantities change, such as the euler lagrange equations, the generalised momenta, mechanical energy and power