How to solve coupled non linear ode using ode 45

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Krishnendu Paul
Krishnendu Paul 2020-5-10
评论： Krishnendu Paul 2020-5-10
I need to solve the following coupled odes, using ode 45.
  1. dthetadt = -(v/Dc)*log(v*theta/Dc);
2. dvdt = (v/a)*((b*v/Dc)*log(v*theta/Dc));
I wrote the following function. but it is not wotking. if u all have time can u give me some guide about to coding with two coupled equations problem
function [t,theta,v] = call_nonlin_ode()
tspan = [0 365];
theta0 = 10;
[t,theta,v] = ode45(@nonlin_ode,tspan,theta0)
function[dtheta,dvdt]= nonlin_ode(t,theta)
a = 0.01;
b = 0.02;
Dc = 1e-5;
v0 = 1e-2;
dthetadt = -(v/Dc)*log(v*theta/Dc);
dvdt = (v/a)*(b*v/Dc)*log(v*theta/Dc);
end
end

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采纳的回答

Bjorn Gustavsson
Bjorn Gustavsson 2020-5-10
When you have a coupled set of ODEs the ode-function has to return a column-vector with the derivatives. So you'll have to modify your function to something like this:
function[dthetadtdvdt]= nonlin_ode(t,theta_v)
a = 0.01;
b = 0.02;
Dc = 1e-5;
v0 = 1e-2;
theta = theta_v(1);
v = theta_v(2);
dthetadtdvdt = zeros(2,1);
dthetadtdvdt(1) = -(v/Dc)*log(v*theta/Dc);
dthetadtdvdt(2) = (v/a)*(b*v/Dc)*log(v*theta/Dc);
end
Then you'll have to modify your call and output-handling correspondingly.
HTH
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Bjorn Gustavsson
Bjorn Gustavsson 2020-5-10
Please read the documentation:
Example
[t,y]=ode45(@vdp1,[0 20],[2 0]);
plot(t,y(:,1));
solves the system y' = vdp1(t,y), using the default relative error
tolerance 1e-3 and the default absolute tolerance of 1e-6 for each
component, and plots the first component of the solution.
There you see that the variable y will have some number of of components, and the first is ploted, you also see that the tSpan used there is from 0 to 20 and that the initial condition has two components - that is an initial conditoin for the first and the second component of y. For your problem where you have 2 coupled equations you will also have 2 initial conditions, one for theta and one for v, and your solution should have 2 columns (the first for theta and the second for v). Your call sould be something like this:
[t, theta_v] = ode45(@(t,th_v) nonlin_ode(t,th_v),tSpan,[theta0, v0]);
which should give you both theta and v as the first and second column of theta_v.
HTH

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