MATLAB: Ode coupled equations solver

differential equationsMATLABode45

Hii Friends,

Is it possible to have a negative values in the parenthesis of ode45 solver?

[z,y] = ode45('Name',[0 1],[y3pmi y3shi]);

e.g. Can y3pmi and y3shi be vectors where in some of the values are negative and imaginary?

Thanks in advance.

Pavan

Best Answer

You mean the initial values of the trajectory? Yes, of course they can have any value. And in Matlab imaginary values are treated exactly as real values.

Simply try it.

Related Solutions

MATLAB: Coupled Differential Equation

Here is an example where someone is using ode45 to solve an even bigger problem. To avoid out-of-memory errors, make A into a sparse matrix if you can.

EDIT: If I understand your notation, M is actually a vector with components M_q, and ditto for K and B. So you should create a new vector

X = [M; N];

and then define your function as follows:

f = @(x) [-gamma*x(1:end-1) + x(end)*B.*(x(1:end-1)+1) - c*K.*x(1:end-1); P - A*x(end) - x(end)*sum(B.*x(1:end-1))];

(or you could create an easier-to-read function in a separate file).

MATLAB: Solving coupled differential equations

For symbolic solutions look at the help for dsolve, for numerical soutions convert the 2nd order ode to 2 coupled first-order odes, then put all 4 first-order ODEs into one function and one of the odeNN (ode45, ode23, etc) with that function, the time-spand and your initial condition. Something like this would be the ODE-function:

function dydt = your_ode(t,y)
w_m = 21; % and so on for your other constants - you could also have them as additional inputs
w1 = y(1);
w2 = y(2);
f  = y(3);
dfdt = y(4);
dw1dt = (w_m - y(3))*exp(f-12t);
dw2dt = (w1 - w2*sin(12*t));
d2fdt2 = f+12*w1-w2; % change to your actual ODEs here...
dydt = [dw1dt;dw2dt;dfdt;d2fdt2];
end

Then call, for example, ode45:

w1_0 = 123;
w2_0 = 231;
f_0 = exp(pi);
dfdt_0 = sqrt(2);
y0 = [w1_0;w1_0;f_0;dfdf_0];
t = [0,37];
[T,w1w2fdfdt] = ode45(@(t,y) your_ode(t,y),t,y0);

HTH

Best Answer

Related Solutions

MATLAB: Coupled Differential Equation

MATLAB: Solving coupled differential equations

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