How to set the number of independent variables of differential equations automatically？

clc,clear;
R = 8.314;
g = 9.8;
N = input('species number:');
for i = 1:N
    name{i} = input('species:','s');
    Mi(i) = input('moler weight of species:');
    m(i) = input('entrance mass fraction of species:');
    rho0(i) = input('initial density of species:');
    mirho0(i) = m(i)/rho0(i);
end
syms T z x
%%
%initial moler concentration
sum_mirho0_1 = 0;
for i = 1:N
    sum_mirho0 = sum_mirho0_1+mirho0(i);
    sum_mirho0_1 = sum_mirho0
end
for i = 1:N
    rho0av = 1/sum_mirho0
    c0(i) = rho0av*m(i)*1000/Mi(i);
end
%%
dTdz = input('temperature gradient(K/m):')
T0 = input('entrance temperature(K):')
T = T0 + dTdz*1000*z;
%thermal diffusion factor
%%
syms z
c = sym('c',[N,1])
sum_c = sum(c);
sum_c01 = 0;
for i = 1:N
    sum_c0 = sum_c01+c0(i)
    sum_c01 = sum_c0
end
%%
for i = 1:N
    alpha(i) = -(log((c(i)/c0(i))*((sum_c0-c0(i))/(sum_c-c(i)))))*(log(T/T0));
    %individual height
    Hi(i) = 1/((Mi(i)*g)/(R*T));
    %ode for every species
    dc(i) = c(i)*(-(27*((1 + alpha(i))/T)-(1/Hi(i))))
end
%%
f = matlabFunction(dc');
F = @(z,c)f(c(1),c(2),z)
%%
[z,c] = ode45(F,[0:0.1:100],[c0(1),c0(2)])

In this code,number of species equals to the number of functions.,for example,if species number is 2,so when I set ode,I should type:

F = @(z,c)f(c(1),c(2),z)

I want to omit this step，how can I modify the code to automatically identify the number of independent variables(c(1),c(2) and so on) and set it in the form that ode equation can identify(it is the form'c(1),c(2)...' rather than 'c1,c2' or others).

Thanks a lot for your help.

Answer 1

[Kartik Saxena]

Hi,

I understand that you want to identify the number of independent variables automatically.

To automate the process of creating a function handle that can be used with `ode45`, you can leverage the fact that the `f` function returned by `matlabFunction` can accept a vector of inputs. This way, you don't need to manually specify each component of `c` when defining the function handle `F`. Instead, you can pass the entire vector `c` to `f`.

Here's a code snippet of how that would look like:

f = matlabFunction(dc', 'Vars', {c, z});
F = @(z, c) f(c, z);
[z, c] = ode45(F, [0:0.1:100], c0(1:N));

Refer to the following MathWorks documentations to for information about the use of 'matlabFunction' and 'ode45':

• https://www.mathworks.com/help/symbolic/sym.matlabfunction.html
• https://www.mathworks.com/help/matlab/ref/ode45.html?searchHighlight=ode45&s_tid=srchtitle_support_results_1_ode45

I hope this resolves your issue.