Generate and solve differential equation? Please suggest some better way if you know.

Hello everyone, I am working on a project and i have to deal with many of differential equations. I am able to generate those differential equations through MATLAB. But, the problem is TIME. It takes a lot of time. Hence I want to save these differential equations in my first run. Then call these differential equations when i need. This would save time in generating the differential equation each time I run my main file.

The variable "n" determines the number of differential equations.AS n Increases, the number of differential equation would be large.

Suppose n=3,there would be four equations generated.

Eqn =[(3*C(1)^2)/250 - (3*C(1)*C(2))/200;
   (3*C(1)^2)/500 - (3*C(1)*C(2))/200;
                   (3*C(1)*C(2))/1000;
                    (3*C(1)*C(2))/250]
%Dimension 0f eqn
                eqn=4 X 1 sym
%I have tried iT with a function

function [dCondT]=trail6(t,C)
load('diffeqn_n_3') %Saved eqn and loaded here
dCondT=sym(zeros(length(Diff_eqns_of_molecules),1))
for n=1:length(Diff_eqns_of_molecules)
    dCondT(n)=[Diff_eqns_of_molecules(n)]
end
end
% then tried solving it with ODE45 

ERROR-"Inputs must be floats, namely single or double.

Can anyone help ?

[madhan ravi]

just upload the latex form of the equations

[P K]

There are no "latex form" of equation. I have made it through loop. So when n increases the number of equations would increase. For n=3, eqn=4 and when n=10, eqn=300,I hope i answered your question.

[John D'Errico]

You need to appreciate a few things.

1. ODE45 is a NUMERICAL ODE solver. It cannot use a symbolic input. Use dsolve for symbolic problems.
2. Bigger problems take bigger time.
3. Large symbolic problems often have no analytical solution.

[P K]

With eval I am able to use ODE45.

[madhan ravi]

Eval is evil see the suggestion below.

[P K]

Thanks @all i would not use Eval but for now i am getting my result through Eval.

Answer 1

[madhan ravi]

As John D'Errico says you may want to use odetovectorfield() and matlabFunction() to convert your symbolic odes to numeric odes.

[P K]

@Walter & @ madhan -if i am getting correct solution, what is wrong in using eval() . It is very conveniently giving the result. I have checked the solution to validate the solution

[madhan ravi]

https://www.mathworks.com/matlabcentral/answers/304528-tutorial-why-variables-should-not-be-named-dynamically-eval

Answer 2

[Walter Roberson]

You are trying to use ode45 with symbolic equations, which is not possible. See odeToVectorField and odeFunction for routines to convert symbolic differential equations for use with the numeric ode* routines.

[P K]

I tried using eval with ode45 and i got the result

[Walter Roberson]

Symbolic expressions are in a language which is not exactly MATLAB. When you eval() a symbolic expression you can get errors -- or even worse, you might not get an error but might encounter a subtle difference. There are some functions for which the parameters mean different things for the numeric function compared to the symbolic function (such as the parameters being in a different order.)