MATLAB: I am solving with ODE45 diff equations system. How can i change a paramter in time for ODE45

solve ode45 paramter function equation change parameter in ode45

hello,

I am solving with ODE45 diff equations system. How can i change a paramter in time for ODE45?

I am solving for z, 1,2,3,4—–and i got a paramter in this equations alfa……after a while i need a different alfa which changes with: alfa=-11782*log(t) + 106989; t is time……so i want to solve ode if my z(2) is a certain calue after that i need alfa t change…..how can i solve this HELP me pls?

% if (z(2)>0.32)    
%   alfa=23950;
% else
% % alfa=-11782*log(t) + 106989;  
% end
tspan=[0 500];
[t,z]=ode45(@dYfdYdXdTgdTp,tspan,[y0 X0 Tg0 Tp0]);

alfa is in this @dYfdYdXdTgdTp function..

so i need something that after z(2) value reaching a certain value…..change my alfa in each step…whith an equation…

Best Answer

If I understand correctly what you want to do, defining ‘alfa’ in your ‘dYfdYdXdTgdTp’ ODE function as:

alfa = 23950.*(z(2)>0.32) - (11782*log(abs(t)+eps) + 106989).*(z(2)<=0.32);

should work.

I added ‘(abs(t)+eps)’ to avoid ‘alfa’ throwing errors if ‘t’ is negative or zero. (Note than with the ODE solvers, negative and zero values for ‘t’ are permitted.) It will not affect your results.

Related Solutions

MATLAB: Using ODE 45 coupled ODEs

Start with what you already have:

syms X(t) y(t) Y 
k = 0.0440;
C_A0 = 0.3045;
epsilon = 2;
alpha = 0.001;
F_A0 = 2.5;
rho = 0.001;
ode1 = diff(y) == -(alpha/2*y)*(1+epsilon*X)*rho;
ode2 = diff(X) == k*C_A0*(1-X)/(F_A0*1+epsilon*X)*y*rho;

then use odeToVectorField and matlabFunction (linked to in that doeumentation) to create your ODE anonymous function.

This appears to be a homework assignment, so I leave the rest to you.

MATLAB: Changing a parameter in a differential equation

Hi Sean,

you can pass the value of epsilon into the ode function with

[tSol,YSol]=ode45(@(t,Y) quantumsystem(t,Y,epsilon),tRange,Y0);

and

function dYdt = quantumsystem(t,Y,epsilon);
    x=Y(1);
    y=Y(2);
    z=Y(3);
    gamma=1/2;
    c=1;
    dtheta=gamma*c/(t^2 + c^2);
    dxdt=(-1/epsilon)*y - dtheta*z; 
    dydt=(1/epsilon)*x;
    dzdt=dtheta*x;
    dYdt=[dxdt;dydt;dzdt];
end

Since ode45 picks the time increments, different values of epsilon may lead to different lengths of tSol and YSol, but the information is there. One of the easier ways to deal with that issue is to set up a for loop with different values of epsilion and use

plot(tSol,z)
hold on

inside the loop as you are doing, only without the color specification.

Best Answer

Related Solutions

MATLAB: Using ODE 45 coupled ODEs

MATLAB: Changing a parameter in a differential equation

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