ODE solver with variable derivative

Question

cameron morrison 2020-4-22

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评论： Bjorn Gustavsson 2020-4-22

This question relates to the function handle to determine the derivative vector for use in ODE45.

My 'dx' changes during each iteration of my code (my dx is dependent on applied forces), as such I need a way of updating the force within the function. A simple example is shown below.

function dx = functionhandle(t,x_current)
dx(1) = x_current(1)*F_x 
end

and then I would call this function handle in my main script to determine the new statespace

[t,x_new] = ODE45(@functionhandle,[0 dt/2 dt],x_current)

where x_new is my updated statespace. My question can be boiled down to this: How do I retreive F_x within the function handle to tabulate dx.

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Answer 1

Bjorn Gustavsson 2020-4-22

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It is rather easy once you've wrapped your head around it:

function dx = forcefunction(t,x_current,Pars4function)
% Example with sinusiodaly varying F:
A = Pars4function(1);
w = Pars4function(2);
F_x = A*sin(w*t);
dx(1) = x_current(1)*F_x;
end

Then you can call your ode-integrator like such:

x0 = 0.1;   % Initial condition
t0 = 0;     % Start-time
tend = 50;  % end-time
A = 2;      % amplitude of force 
w = 1/2/pi; % angular frequency
t_span = linspace(t0,tend,5001);
[t,x_all] = ode45(@(x,t) forcefunction(t,x,[A,w]),t_span,x0);