Coding a second degree differential equation

Hello,

I am trying to code a nonlinear second degree differential equation with 2 boundary conditions.

I have included a screenshot of the equation where ?_r is a function of C. ?_0, z, and F are constants. The system is 1-D.

I am having trouble coding phi, since I don't have a function of "phi=..." and even if I want to use diff(phi,2), I don't know how to code abstractly with variables.

[darova]

What are and ? Where are they?

[Rojan Parvaresh]

C is for concentration . z_i is charge which is constant for each species of i. For example z of OH- is -1.

Regarding C, there is another transient equation that I was able to code. I have attached the equation.

So the previous equation and the transient equation need to be solved simultaneously and i'm having trouble coding the d^2(phi)/dx^2 equation from above

P.S. D_i is the diffusion coefficient which is also a constant for each species i.

Answer 1

[Dhananjay Kumar]

You can declare phi as a symbolic variable by using syms command and sove the equation symbolicaly as we solve any equation by hand.

See examples here: https://in.mathworks.com/help/symbolic/solve-a-system-of-differential-equations.html#responsive_offcanvas

[Rojan Parvaresh]

Hi, so I'm still having trouble even with using syms.

I have attached my code and you have the equations, I keep getting an error in my for loop

[Dhananjay Kumar]

Hey, as I mentioned Symbolic variables are used to sove equations or evaluate expressions symbolically (the way we differentiate/integrate functions on our notebooks).

Suppose you want to get derivative of cos(x), then you do this:

>> syms x;

>> syms y(x); (This statement tells MATLAB that y is a function of x)

>> y = cos(x)

>> yd = diff(y)

This gives you yd = -sin(x).

If you want to evaluate value of the symbolic expression/function, you should use subs function (not like cos(pi), the way you have written in the code).

In your code, you first need to declare x as symbolic variable. Also, to declare a function c dependent on t, t should be symbolic not a constant value.

Please read the documentation and go through the examples to get more abstract view.