# Using SOLVE with large number of equations and variables

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M.P. on 2 Jan 2020
Answered: Pujitha Narra on 6 Jan 2020
Is there a way to use the command X = solve([eqn1, eqn2, eqn3, [x1 x2 x3]) for very large number of equations and variables without typing explicitly :equ1, equ2, equ3 and x1,x2,x3? The equations are Kirchoff's loop and node equations and the variables are the currents.

J. Alex Lee on 2 Jan 2020
Edit: didn't see the rest of the question...I guess that depends on if there is a regular pattern in the circruit that would allow reducing your equations into a smaller set of rules.
Wouldn't the resulting set of equations be linear so that there would be no need to invoke a complicated solver?
M.P. on 3 Jan 2020
Yes, there is a pattern. I have a square grid of resistors (all of them different from each other). I want to make the grid as big as I can (thousands maybe). Is there another method other than solve or linsolve? I have heard about iterative methods but I do not know how to get started.
J. Alex Lee on 6 Jan 2020
Your problem seems not to be about solving the system (using direct versus iterative methods), but rather about the programming to sett up the problem. Also, I think I'm out of my depth if you are wanting to use symbolic toolbox.
Generally, if you have rules governing your equations, you can use things like loops to efficiently code them in.

Pujitha Narra on 6 Jan 2020
As far as I understand, you are looking for simpler way to solve the Kirchoff's loop equations.
In your case, it is right that you could use iterative methods. Especially Gauss-Seidel and Jacobian methods would be of great help for solving Kirchoff's loop equations as far as I know. These are good for sparse matrices.
The following link would lead you to a MATLAB File Exchange page which could help you get started with the above mentioned iterative methods. Please note that MATLAB File Exchange is community based and any further queries regarding the code can be directed to the author.