Error function optimisation method to calculate the velocity of a travelling wave

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UserCJ 2023-9-10

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编辑： Torsten 2023-9-11

Hi everyone, I'm trying to use an error optimisation method using interpolation and least quare method for a travelling wave solution. I have a mat file (SS) of size 10000*200 where time steps are defined by rows and node number is defined by columns. In this simulation, there are 10000 timesteps and 200 nodes. These values provide a travelling wave solution as follows.

To calculate the velocity of these waves, I'm trying to use the error optimisation method as given in the pseudo code below.

I tried coding that as follows, however, i'm having a trouble understanding and defining "c" in the anonymous function in the code.

v_t= zeros(Tmax-1);
sol_current = SS(1,:);
%x1= 1:Tmax/200:Tmax;
xq = linspace(0,1,200);
for n=1:length(Tmax)
    sol_future = SS(n+1,:);
    fun=@(c)...
end

It would be great if anyone can help me to code this method. Thank you!

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回答（1 个）

Torsten 2023-9-10

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编辑：Torsten 2023-9-10

For each of the 200 times, extract the node number where your solution equals 0.5. Plot node number as a function of time. The slope of this (in your case most probably linear) curve gives the wave speed.

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Torsten 2023-9-11

编辑：Torsten 2023-9-11

在 MATLAB Online 中打开

In order to apply "interp1", the vector vec must be strictly monotonic. I hope that restricting the interpolation to values > 0.2 and < 0.8 will be successful to achieve this. Otherwise you have to include your data or experiment for yourself.

I assume N = 0:199, am I right ?

pos = zeros(10000,1);
for it = 1:10000
    vec = SS(it,:);
    idx = vec > 0.2 & vec < 0.8;    
    pos(it) = interp1(vec(idx),N(idx),0.5);
end
plot(t,pos)

Star Strider 2023-9-11

In my approach to this problem (Answer, and a subsequent Comment with a slightly different implementation), I define a narrow range of indices to interpolate over (‘idxrng’ in that code) in each iteration of the loop. That usually works to eliminate the non-unique values problem, although I do not have the actual data mentioned here to experiment with.

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