How to solve coupled non linear ode using ode 45

Question

Krishnendu Paul 2020-5-10

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https://ww2.mathworks.cn/matlabcentral/answers/524449-how-to-solve-coupled-non-linear-ode-using-ode-45

评论： Krishnendu Paul 2020-5-10

采纳的回答： Bjorn Gustavsson

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I need to solve the following coupled odes, using ode 45.

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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Answer 1

Bjorn Gustavsson 2020-5-10

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https://ww2.mathworks.cn/matlabcentral/answers/524449-how-to-solve-coupled-non-linear-ode-using-ode-45#answer_431622

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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 2020-5-10

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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

Krishnendu Paul 2020-5-10