Solving a system of differential and algebraic equations

Hello. I would like to solve a system of differential and algebraic equations. The 2 main differential equations are attached in the screenshot. How do I go about solving a system of differential and algebraic equations?

Thanks in advance.

[Torsten]

https://de.mathworks.com/help/matlab/math/solve-differential-algebraic-equations-daes.html

You differentiate with respect to different variables (A and w) ? What does that mean ?

[Zain Shabeeb]

The system is a rectangular block as shown in the attached photo. w is the width the rectangle. A is the area.

I will attach a photo of a similar model in my next comment to make things clearer

[Zain Shabeeb]

Here I have attached a photo of another model. To answer your question, the two different variables here are the direction x and the direction z. The change in the direction of x is a solid phase concentration whereas the change in the direction of z is a liquid phase concentration.

[Zain Shabeeb]

In both of these models, the authors have stated that first the differential equations were discretized into differential algebraic equations using the finite difference method, resulting in coupled non-linear algebraic equations, and then those were solved. If you could help me with this procedure it would be a huge help.

Thanks.

[Torsten]

The equations from your first post and the picture from your third post don't correspond to each other.

First write down your set of equations you are trying to solve together with initial and boundary conditions. Then maybe someone can help.

[Zain Shabeeb]

Hi Torsten,

Thank you for your reply.

I have tried putting together my set of equations. Please look at my most recent post today. Any help would be greatly appreciated.

Thanks.