What are the limitations of using electrical circuits to solve PDEs?

[Domenico94]

Hi everyone. In electrical engineering, when you study control theory, you're taught that electrical circuits can be used to simulate the behaviour of complex systems. What I don't understand is, what are the limitation of this sistem, and why it can't be obviouslly used in a general way to solve PDEs? Does it give only numerical and not analitical solutions?

 

[BvU]

All computers are electrical circuits, so your teachings were correct. Or are you asking this question for analog circuits (as opposed to digital circuits) in particular ?

Anyway, there are obvious size limitations.

And who claims they can't be used in a general way ?

 

[Domenico94]

Yes, it is true that they are, but I was asking it in the sense of using analog circuits, like capacitors, inductors,eventually diodes, to actually find a solution for Partial differential equations. There are engineers, like one named Leon Chua, who did significant work in solving equations using this approach. The thing I wanted to ask is, if it was so easy (Example : I want to solve a PDE, so I build the circuit and see how that works), we would all to this, but I guess it's not so simple as it appears, so what are the problems concerned with this kind of approach? Can be used for analitical solutions or for numerical solutions only?

 

[Mark44]

(Example : I want to solve a PDE, so I build the circuit and see how that works)

I've seen lots of examples of simple electrical systems modeled by ordinary differential equations (ODEs), but haven't seen any that were modeled by partial differential equations (PDEs). In the examples I've seen the voltage and current were functions of t alone. Did you mean ODEs instead of PDEs, or do you have some example where the current and voltage were functions of two or more variables?

I'm not an electrical engineer, so there might be some examples that I'm not aware of.

 

[Domenico94]

I've seen lots of examples of simple electrical systems modeled by ordinary differential equations (ODEs), but haven't seen any that were modeled by partial differential equations (PDEs). In the examples I've seen the voltage and current were functions of t alone. Did you mean ODEs instead of PDEs, or do you have some example where the current and voltage were functions of two or more variables?

I'm not an electrical engineer, so there might be some examples that I'm not aware of.

No, I don't mean electrical circuits being modeled by ODE, of course there are, but I was asking about the inverse problem, when we can model PDEs with electric circuits ( like Leon Chua did, for example)

 

[Domenico94]

Other answers??

 

[BvU]

like Leon Chua did, for example

This man is so productive that he lists 767 references for CHua's circuit and chua's equation alone (in 2004). Plus his own publications, another 459. Could you narrow it down a little and explain what you are referring to ?

I mean, you can try to approximate PDE solutions with electric circuits, but that's not what you mean, is it ?

Re post #1: is it clear that you definitely don't get analytical solutions ?

 

[Domenico94]

Hi ByU :)
I was referring about the fact of solving nonlinear PDEs electric circuits, in a way like Chua did.
No, that's what I was not clear about...I just wanted to ask about the possibility of solving them analitically, or if it isn't feasible at all...Just for curiosity, nothing more :)

 

[BvU]

Found some http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=473591&url=http%3A%2F%2Fieeexplore.ieee.org%2Fiel4%2F81%2F9993%2F00473591.pdf%3Farnumber%3D473591 on Cellular Neural Networks but http://www.functionaldifferentialequations.com/index.php/fde/article/viewFile/197/160complain the results can't be used in real life (low precision, ..) and they change over to digital emulation.

 

[Domenico94]

Cellular Neural Networks...It's always Chua's work, isn't it?