Question
Hi everyone, I have a travelling wave solution drawn at each time step for a set of data obtained from a previous simulation. Tmax = 10000; m =load('solution.mat'); SS = m.sol; N = m.N1; for i = 1:50:Tmax Xval = SS(i,N); hold on plot(N,Xval,'Linewidth',2); end hold off and below is the out put I got from the above code where x axis represents a distance (N) from 0 to 200 and y axis takes values between 0-1. .Each coloured line is drawn at a different time step. Next, I'd like to calculate the velocity at each time step when y=0.5. I.e. I want to identify the x value when y=0.5 for each colour line and calculate the velocity as . The main question here is sometimes there are no exact points in Xval with value 0.5 or no exact N value associated to 0.5. I'd be happy if someone could help me in creating a loop for this calculation.
Expert Answer
Prashant Kumar
PhD Expert
Answered Aug 23, 2026
A simple intersection approach works —
t = linspace(0, 25, 450);
x = sin(2*pi*t+rand(size(t)))/2+0.5;
L = numel(t);
xval = 0.5;
tidx = find(diff(sign(x-xval))); % Approimate Intersections
for k = 1:numel(tidx)
idxrng = max(1,tidx(k)-1) : min(tidx(k)+1,L);
tv(k,:) = interp1(x(idxrng), t(idxrng), xval); % Exact Interseections
end
xv = ones(size(tv)) * xval;
Velocity = 1 ./ diff(tv);
Results = table(tv(2:end), Velocity, 'VariableNames',{'Time','Velocity'})
Results = 61×2 table
Time Velocity
_______ ________
0.86599 2.0118
1.4494 1.7142
1.9056 2.1916
2.4067 1.9959
2.8642 2.1857
3.3668 1.9895
3.8813 1.9438
4.3854 1.9837
4.8913 1.9769
5.4618 1.7527
5.8731 2.4316
6.4307 1.7934
6.8758 2.2465
7.3968 1.9195
7.8853 2.0469
8.3841 2.0048
figure
plot(t, x, 'DisplayName','Original Data')
hold on
plot(tv, xv, 'xr', 'DisplayName','Exact Intersections')
hold off
grid
legend('Location','best')
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