Solving System ODE with ode45

Hi All, I'm trying to solve a system ODE with ode45. I get this error for my code:

Error in ode45 (line 115) odearguments(FcnHandlesUsed, solver_name, ode, tspan, y0, options, varargin);

Any help is appreciated. I have attached the m.files

[bio lim]

I don't see your .m files.

[Donrad]

Whoops. Files are now attached, thanks for the heads up.

Answer 1

[bio lim]

With first look, in your function, there are many undefined variables, that are X0, y0, z0, and Ap0.

[Donrad]

But I have defined those in EnzymaticOscillationORP.m before calling the function.

%The Initial Conditions

 X0=.167 ;
 z0=1.5 ;
 y0=0.0002;
 Ap0=0.22 ;

[Donrad]

Ok, now I see I added those lines to the function file and it worked but there is a warning:

Warning: Failure at t=1.288951e-02. Unable to meet integration tolerances without reducing the step size below the smallest value allowed (2.775558e-17) at time t.

should I change the RelTol?

[bio lim]

Functions do not use base workspace. They use their own workspace; which means you have to define all those variables inside the function. You can declare them as global variables, however it is highly unrecommended.

[Donrad]

I see, Thank you so much.

[bio lim]

That warning is probably due to your system being stiff. I wouldn't suggest you to change the relative tolerance, though I am not sure. I suggest you to use ode15s, or ode23s.

[Donrad]

I'm expecting to see an Oscillation in my system (as in the image). I used ode15s but got the same warning.

[bio lim]

I would try increasing the tolerance then, it may be too 'tight' at the moment. Otherwise, there may be a problem with your system definition.

[Donrad]

Problem was in the initial conditions. Reduced them to reasonable values but Matlab still in busy mode. I don't if the coding was efficient or not. I'm new to Matlab so I just read the documentation of ode45 and wrote the codes.

[bio lim]

I see. Defining unnecessary variables is the first thing you should avoid.

You have defined:

Tg=1;
Tr=2;
ProInh2=3;
HGlnInh=4;
Inh=5;
TrTg=6;
p2_Tr=7;

and then:

x0(Tg)=1;
x0(Tr)=1;
x0(ProInh2)=0;
x0(HGlnInh)=1;
x0(Inh)=0;
x0(TrTg)=1;
x0(p2_Tr)=0;

These are simple things you should avoid. Just set x0(1) = 1, or even better x0 = [1 . . . ], and make a comment saying the first element of your initial condition is Tg. Declaring many variables like this makes your program look very complicated and tiring to look at, especially for debugging. For example, when I was looking at your function definition, I had hard time following it due to the number of variables, and which index is being manipulated in your operations.

[Donrad]

Yeah, I used the proper I.Cs:

x0(Tg)=0.167;

x0(Tr)=0.0002;

x0(ProInh2)=1.5;

x0(HGlnInh)=0;

x0(Inh)=.278;

x0(TrTg)=0;

x0(p2_Tr)=0;

But no solution so far. I agree I have to code efficiently.