Could anyone help me with this warning please?

This is my code :

function RunLogOscilNumeric3

k =10;

p0 =0.1;

t =(0:0.01:10000);

omega = 1;

N0 = 1;

[t,p]=ode23(@logOscilnumeric3,t,p0,[],omega,k,N0);

        Pmax = max(p)

        Pmean = mean(p)

figure(1)

plot(t,p)

title('The plot of the system with time')

xlabel ('Time')

ylabel ('The system' )

1;

% function dpdt = logOscilnumeric3(t,p,omega,k,N0)

% dpdt = N0*p - (N0*sin(omega*t)*p.^2/k);

% end

Notes: 1- Warning: Failure at t=5.060889e+00. Unable to meet integration tolerances without reducing the step size below the smallest value allowed (1.421085e-14) at time t.

2- I tried to change the ode solver ,,but I still got this warning.

3- I want to solve this system for the specific values of the parameters and time'' I do not want to change those at all'' ,, because I am trying to solve different systems for the same parameters and time vector.

What should I do please?

Thanks in advance.

Answer 1

[Torsten]

The analytical solution for your ODE is given by

p(t)=20*exp(t)/(exp(t)*(cos(t)-sin(t))-201)

This function has a singularity between t=5 and t=5.5.

Best wishes

Torsten.

[Avan Al-Saffar]

Many thanks. OMG singularity again,,it is like a bad dream for me!!! Do you have any suggestion please?

[Avan Al-Saffar]

Dear Torsten

When I solved the above system by details, I got this result which is different from yours,, Could you check it again please??

My result is : p(t)=20*exp(t)/(exp(t)*(sin(t)-cos(t))+1)

[Torsten]

The initial condition is not satisfied for your solution: p(0)=0.1.

Best wishes

Torsten.

[Avan Al-Saffar]

So what is the initial condition that you used to find the above result please?

[Torsten]

Sorry, I overlooked a minus sign:

p(t)=-20*exp(t)/(exp(t)*(cos(t)-sin(t))-201)

is the solution of the ODE

p'(t) - (p(t)-Sin[t]*p(t)^2/10) = 0, p(0)=0.1

Best wishes

Torsten.

[Avan Al-Saffar]

Dear Torsten If I have the following system : dx/dt = N0*sin(omega*t)*x - (N0*x.^2 / k)

I tried to solve it analytically but I am getting this formula which I can not continue:

( exp( (-N0/omega)*(cos(omega*t)) )/x)= ( integral( (N0/omega) * (exp( (-N0/omega) * (cos(omega*t)) )) )dt )

can you help me please?

Regards

[Torsten]

Try MATLAB's dsolve.

If an explicit solution can not be found, you will have to solve the equation numerically for given values of N0, omega and k.

Best wishes

Torsten.