MATLAB: Using odesolver with functions that have many inputs

differential equations

I'm trying to use ode45 to integrate a first order differential equation. The first line of my function m-file is

function dEds = dPdE(s, E, U0, H0, mu, T, t, initial, final,timestep)

s is my independent variable, and E(s) is what I am solving for. All the other variables are matrices or scalars, and are used in the m-file. My question is, when using ode45, how do I specify these other variables? On this page

<http://www.mathworks.com/support/solutions/en/data/1-1C6YS/index.html?product=ML&solution=1-1C6YS>

other inputs are being put in after the (blank) options, and I verified for myself that it can work, but I haven't seen any documentation refer to that. Furthermore it doesn't seem to be working when I try and solve my equation:

[s E]=ode45(@dPdE,[0 5],E(321),[],U0,H0,mu,5,3.2,2,3,.01);

It says too many input arguments. How can I make this go?

(A more trivial question I have is whether I need to put s as an input argument if the function never uses it.)

Best Answer

The documentation in the link you provide probably applies to an older version of MATLAB than you have. Instead, create an anonymous function:

f = @(s,E) dPdE(s, E, U0, H0, mu, T, t, initial, final,timestep);

Then you can solve the equation using

 [s, E]=ode45(f,[0 5],E(321));

Yes, you do need to provide s as an input argument.

Related Solutions

MATLAB: Event function with odesolver error

Ah. I think I have an idea now. Check the error message trace. I'm guessing the error actually occurs within Schrodinger. When ode45 passes E into the ODE function dPdEfull or the event function Pifevent, it passes just the current timestep's value, so E is a column vector (even though the E returned by ode45 is in the form of a matrix). Inside dPdEfull you call Schrodinger:

a=Schrodinger(t,U0,H0,mu,E);

and here E is a vector and all is well. But inside Pifevent you call

u=Schrodinger(t,U0,H0,mu,E(end,:));

Because E is a (column) vector, E(end,:) is the last row, which is a scalar. If Schrodinger expects a vector as the last argument, that could cause an error like you're getting.

MATLAB: Solving a system of higher order differential equations with ode45 …error

Try this:

syms g(n) f(n) n Y 
%
C=g^-(1/3);
Pr=.7;
gamma=1.4;
Me=3;
gw=1+sqrt(Pr)*((gamma-1)/2)*(Me^2) %Taw/T_e
EQ1=diff(C*diff(f,2))==-f*diff(f,2);
EQ2=diff((C/Pr)*diff(g))+f*diff(g)+(C*(Me^2*(gamma*(gamma-1))))*diff(f,2)^2==0;
EQS=[EQ1 EQ2];
[V, Vsubs] = odeToVectorField(EQS)
n=[0:1:1E+2];
M = matlabFunction(V,'vars', {'n','Y'});
% ICs=[f(0)==0,diff(f(0))==0,diff(f(0),2)==.75,g(0)==gw,diff(g(0))==.75] %not sure how to apply the 5 IC's to correspond to V - when i run this i get error div/0 - but oddly enough if I change around the order of the IC's the error is replaced with inputs must be type double, but then I get all NAN results I must be doing something really wrong. %
ICs = [gw; 0.75; 0; 0.75; 0.75];
Sol = ode45(M,[n(1) n(end)],ICs)
figure(1)
semilogy(Sol.x, abs(Sol.y))

This runs, although you will probably need to be certain all the variables have the appropriate initial conditions.

I tweaked your code just a bit, adding ‘Vsubs’ to the odeToVectorField output to guarantee that I understand the ‘Y’ variables that correspond to the functions and derivatives. I then did the best I could to match them with the ‘ICs’ vector.

I added the plot. You will need to change it to provide the correct (and easily understandable) variables.

I didn’t see this earlier today, so I thank you for bringing it to my attention. (I generally don’t reply to private messages.) Your Question is straightforward, well-stated, and (I hope) easily solved!

Best Answer

Related Solutions

MATLAB: Event function with odesolver error

MATLAB: Solving a system of higher order differential equations with ode45 …error

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