How to use if statement with ode23

Question

Joanie 2017-9-15

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/356811-how-to-use-if-statement-with-ode23

编辑： Walter Roberson 2017-9-20

I have a formula in the form of:

dy/dt = f - a*y
f(t) = x-k*t

I can use the ode23 function to solve this for both:

x = 2;
a = 3;
x1 = 4;
a1 = 5;
Tb = 0;
Te = 0.6;
Ti = 0.15;
F = @(t,y) (f*t)-(a*y);
[t,y] = ode23(F,[0 0.6],0);
F1 = @(t,y) (f*t2)-(k*y2);
[t2,y2] = ode23(F1,[0 0.6],0);

When f(t) is between min en max use formula 1, if f(t) is between max and min use formula 2.

Hope someone can help me out here.

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Walter Roberson 2017-9-15

Your F1 uses t2 and y2 before they are defined.

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Answer 1

Jan 2017-9-15

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链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/356811-how-to-use-if-statement-with-ode23#answer_281665

在 MATLAB Online 中打开

ode23 can handle smooth functions only. See Answers: Discontinuities in ODE45 . The only reliable solution is an event function, which stops the integration and restarts it with the current values and the new function. See https://www.mathworks.com/help/matlab/math/ode-event-location.html

F1  = @(t,y) (f*t)-(a*y);
F2  = @(t,y) (f*t2)-(k*y2);
opt = odeset('Events', @(t,y) DetectEvent(t, y, minValue, maxValue));
t   = Tb;
y0  = 0;
while t < Te
  if "y is inside the interval"   % (This is not clear in your description)
    F = F1;
  else
    F = F2;
  end
  [tt, yy] = ode23(F, [t, Tb], y0, opt);
  t  = tt(end);
  y0 = yy(end);
  ... some code to collect the yy values
end

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m4 Chrennikov 2017-9-15

Hmmm, my fault. The only reason I want to use sol struct is that I use deval function to process ode solution. If you inspect its source code you can see that it utilizes not only data mentioned above but some 3d matrix sol.idata.f3d. My idea for next day was to try to concat this this matrix if there's no out-of-box solution. Hope I was clear enough)

m4 Chrennikov 2017-9-20

在 MATLAB Online 中打开

works for me:

function sol1 = concatSol( sol1, sol2 )
%CONCATSOL Summary of this function goes here
%   Detailed explanation goes here
if ~strcmp(sol1.solver,'ode45')
    error('ode45 solver required')
end
if ~strcmp(sol1.solver,sol2.solver)
    error('sol1 & sol2 sovers are not the same')
end
sol1.x = [sol1.x, sol2.x(2:end)];
sol1.y = [sol1.y, sol2.y(:,2:end)];
sol1.xe = [sol1.xe, sol2.xe];
sol1.ye = [sol1.ye, sol2.ye];
sol1.ie = [sol1.ie, sol2.ie];
sol1.stats.nsteps = sol1.stats.nsteps + sol2.stats.nsteps;
sol1.stats.nfailed = sol1.stats.nfailed + sol2.stats.nfailed;
sol1.stats.nfevals = sol1.stats.nfevals + sol2.stats.nfevals;
sol1.idata.f3d = cat(3,sol1.idata.f3d,sol2.idata.f3d(:,:,2:end));
end