What is the origin of "Weissinger Implicit ODE"

In the ode15i tutorial, the first example is titled "Weissinger Implicit ODE". Could you explain the physical process this equation models and provide information about its origin? I’ve searched for references but haven’t been able to find any that describe this equation in detail.

[KALYAN ACHARJYA]

Have you checked the reference paper "Lawrence F. Shampine, “Solving 0 = F(t, y(t), y′(t)) in MATLAB,” Journal of Numerical Mathematics, Vol.10, No.4, 2002, pp. 291-310."?

[Torsten]

I doubt that the physical background of an example equation is explained in this numerical paper.

[Jonas]

No it's not mentioned in the paper at all. I've also read all the published lecture notes of Johannes Weissinger, but the equation is not given there.

[Torsten]

@Jonas

I'd simply contact MATLAB Support:

https://uk.mathworks.com/support/contact_us.html

If TMW uses the equation as example, they should know its source.

Answer 1

[John D'Errico]

I usually laugh at the results of the AI tools available. Half the time they are blowing smoke, since they don't really understand the mathematics involved. And I can recall some great examples, where such a tool gave an answer that was completely incorrect, just total mathematical word salad BS.

Regardless, I threw your question into an AI tool (Poe). It said this:

The Weissinger Implicit Ordinary Differential Equation (ODE) refers to a specific approach in numerical methods for solving ODEs. It’s typically associated with the Weissinger method, which is an implicit method used for solving ordinary differential equations, particularly for stiff systems.Key Features of the Weissinger Implicit Method:

1. Implicit Nature: Unlike explicit methods, where the next step is calculated directly from the previous step, implicit methods require solving an equation that involves both the current and next steps.
2. Stability: Implicit methods are generally more stable than explicit methods, especially for stiff ODEs. This means they can handle larger time steps without becoming unstable.
3. Applications: Commonly used in engineering and physics where stiff equations arise, such as in chemical kinetics or certain mechanical systems.
4. Formulation: The general form can be represented as:yn+1=yn+hf(tn+1,yn+1),yn+1​=yn​+hf(tn+1​,yn+1​),where yn+1yn+1​ is the unknown at the next time step, ynyn​ is the known value, hh is the step size, and ff is the function defining the ODE.
5. Iterative Solution: Because of the implicit nature, methods like Newton's method are often used to solve for yn+1yn+1​.

Feel free to take it as worth what I spent on it.

[Jonas]

That is not even related to the question. Weissingers equation is given by `0 = t*y^2 * yp^3 - y^3 * yp^2 + t*(t^2 + 1)*yp - t^2 * y`. I know Johannes Weissinger developed numerical methods but the equation is not related to a numerical method your AI tool mentioned.

NB: The method given is the implicit Euler method. I doubt it was developed by Johannes Weissinger.

[John D'Errico]

As I said, it need not be trusted, coming from an AI tool. As I said, worth what it cost.

That you cannot find anything, might suggest you are looking in the wrong places, or the wrong way. Very often search engines are highly sensitive to posing the correct question, in a very specific way.

Were I you, I would start with the Shampine paper. If it is described there, then that paper will probably have a reference you can read. Or you can contact tech support as has been suggested.