Trouble with ODE45

Hi,

I've got a problem solving my ODE45 function. I have the equation d^2x/dt^2 - sigma^2*x = F(t), meaning the right hand side is a vector. F(t) is an equation containing data from an experiment. To simplify lets say F = 1:1:81.

I have converted the ODE into a first order ODE with x1' = x2 and x2' = F - sigma^2*x1. sigma = 2*pi/t

t = linspace(3.6,7.2,81); %time vector 
F = 1:1:81; % Right hand side

initial_x    = 0;
initial_dxdt = 0;

[t,x] = ode45(@funct,t,[initial_x,initial_dxdt]);

plot(t,x(:,1));
xlabel('t'); ylabel('x');

function dxdt = funct(t,x) 
dxdt_1 = x(2);
dxdt_2 = F - (2*pi/t)^2*x(1);

dxdt = [dxdt_1;dxdt_2];
end

What I am trying to do is to change the value of F for every value of t, but it seems that I cannot insert any values of add variables into "funct" without getting massive error messages. Do I have to insert ODE45 into a for-loop? Or is there something that I am missing? Thanks in advance

Answer 1

[Jan]

It looks like F is not smooth. Then Matlab's integrators cannot handle this directly, see https://www.mathworks.com/matlabcentral/answers/59582-ode45-errer-input-argument-y-is-undefined#answer_72047.

The best way is a loop:

t = linspace(3.6,7.2,81); %time vector 
F = 1:1:81; % Right hand side
x0 = [0, 0];

t0 = t(1);
for iStep = 2:numel(t)
  Fs = F(iStep - 1);  % For example
  [ts, xs] = ode45(@(t, x) funct(t, x, Fs), [t0, t(iStep)], x0);
  t0 = ts;
  x0 = xs(end, :);
  % Store ts and xs for the output...
end

function dxdt = funct(t,x, F) 
dxdt = [x(2); ...
        F - (2*pi/t)^2*x(1)];
end

This is untested and thought to show the concept only.

[Christian Kosacki]

Okay right, I will look into that. Thanks for the help!