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In this question we are asked to denote a matrix linear system of form:

`AY = F`

I understand `Y`

are the solutions of the PBE Eq at the evaluated points. For example the Gouy-Chapman in the forms of
`tanh(ze\psi/k_b T) = \Lambda _0 exp(-\kappa x)`

, so we could use these as guess solutions for the starting solutions.

But I do not understand what `f(x_i)`

is, would this be the RHS of the PB equation, i.e.:

`\sum _j \frac{e}{\epsilon _0 \epsilon _r}exp(-z_j e \psi (x_i) / k_B T)`

Also, I noticed that in the enunciate of the problem you set that we are solving:

`- \frac{d^2\psi}{dx^2} = f(x_i)`

Why have we moved the sign here to the LHS? Is this so that the coefficients for the A matrix match accordingly?

Finally, I do not understand what `\alpha`

and `\beta`

are. Are these simply the BC conditions at x=[0, H]? So we would have the same potential at both ends?

To enable design management, you'll need to meet the requirements. If you need help, reach out to our support team for assistance.