ODE45: how to print a variable

Hi, I have the following code

.m file

function vdot=diffeq(t,v)
a=2;
b=3;
c=4;
d=5;
e=a*b/c;
%
vdot=zeros(2,1);
vdot(1)=v(2);
Delta=e*b*v(2)*sqrt(t);
vdot(2)=0.5*v(1)+3/4*v(2)+sin(t)+Delta;

run.m file

R0=510e-6;
tf=40e-6;
options = odeset('RelTol',1e-8,'AbsTol',[1e-8 1e-8]);
[t,v]=ode45('diffeq',[0,tf],[R0,3],options);
[t,v(:,1)]

How can I print the variable Delta in the command window and afterthat export it to an Excel file? At the moment I cannot simply type in filename='excel_file.xls'; xlswrite(filename,Delta)

Thank you.

Answer 1

[Jan]

function [vdot, Delta] = diffeq(t,v)
a=2;
b=3;
c=4;
d=5;
e=a*b/c;
%
vdot       = zeros(2, numel(t));
vdot(1, :) = v(2, :);
Delta      = e * b * v(2, :) .* sqrt(t);
vdot(2, :) = 0.5 * v(1, :) + 3 / 4 * v(2, :) + sin(t) + Delta;
end

Now integrate as before and afterwards request Delta only for the accepted time steps:

[t, v]      = ode45(@diffeq, [0,tf], [R0,3], options);
[vt, Delta] = diffeq(t.', v.')

[Marco Sammito]

@Jan Could you explain to me what vt means in [vt, Delta] = diffeq(t.', v.')

[Walter Roberson]

I am surprised this works. My tests with anonymous functions seemed to imply that you cannot have multiple outputs for the objective function.

[Jan]

@Marco: "vt" means "v transposed".

@Walter: When called from ODE45, the Delta output is ignored. It matters only in the specific call after the intergration. This can be triggered explicitly:

function [vdot, DeltaOut] = diffeq(t, v)
a=2; b=3; c=4; d=5; e=a*b/c;
vdot       = zeros(2, numel(t));
vdot(1, :) = v(2, :);
Delta      = e * b * v(2, :) .* sqrt(t);
vdot(2, :) = 0.5 * v(1, :) + 3 / 4 * v(2, :) + sin(t) + Delta;
if nargout > 1
  DeltaOut = Delta;
end
end

I do not see the relation to anonymous functions.

Answer 2

[Walter Roberson]

The ode*() routines, when processing with multiple variables (e.g., your v is length 2), do not proceed in a linear fashion over time: they need to explore different boundaries at the same time point. The ode*() routines also do not simply sample at a bunch of times and v values and report at the locations that they sampled at: they probe at a variety of locations and use that to interpolate at the times that they report about.

It is therefore not beneficial to just output the delta values: you would need to also output the t and v values so you would have the context for the delta values.

The best way to record values like these is to use nested functions with shared variables:

function run

    R0=510e-6;
    tf=40e-6;
    options = odeset('RelTol',1e-8,'AbsTol',[1e-8 1e-8]);

    guess_at_iterations = 10000;

    Iters = 0;
    recordings = nan(guess_at_iterations, 4);   %shared variable!

    [t,v]=ode45( @diffeq, [0,tf], [R0,3], options);
    [t,v(:,1)]

    recordings_cell = [{'t', 'v1', 'v2', 'delta'}; num2cell(recordings(1:Iters,:))];
    xlswrite('YourFile.xlsx', recordings_cell);

    function vdot=diffeq(t,v)
      a=2;
      b=3;
      c=4;
      d=5;
      e=a*b/c;
      %
      vdot=zeros(2,1);
      vdot(1)=v(2);
      Delta=e*b*v(2)*sqrt(t);
      vdot(2)=0.5*v(1)+3/4*v(2)+sin(t)+Delta;

      Iters = Iters + 1;
      recordings(Iters, :) = [t, v, Delta];
    end   %this must be here to match the function

end   %this must be here after everything else

[Jan]

@Walter: "run"? Like the built-in function to start scripts?

Collecting the values inside the function to be integrated includes the values of rejected steps.

[Walter Roberson]

Ah, yes, wasn't thinking. I was just grabbing the name the poster had used, to show that it was all one file.

[Walter Roberson]

The line

        recordings(Iters, :) = [t, v, Delta];

should be

        recordings(Iters, :) = [t, v.', Delta];

Answer 3

[Marco Sammito]

Thank you for answering. I tried your code but MATLAB returns this error:

[Jan]

Please post comments in the comment section, not as an answer and prefer text copies instead of screenshots. Thanks.