# gradient of a gradient giving drastically different answer than the del2 operator

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I took a derivative of a derivative using the gradient method. I then applied the del2 operator to take the second derivative directly. For some reason, the second derivative calculated by taking gradient twice does not at all match that of the del2 operator. The gradient of a gradient method seems to be correct, and the del2 operator just shows a continuously decreasing function (which is wrong). Could anyone take a look at my code and figure out what I am doing wrong with the del2 operator? I also have attached ex.txt so that you can directly compute everything that I am seeing. I also attached the figure that is produced. You can see that the graph on the left (gradient of a gradient) is very different than the del2 method (right graph)

filename = 'ex.txt';

delimiterIn = ' ';

headerlinesIn = 5;

% Import the data file for post-processing

matrix = importdata(filename,delimiterIn,headerlinesIn);

A = matrix.data;

A = A(:,1:3);

%Define the number of distinct isotherms

temp_ids = sum(A(:) == 0.2);

%Define the number of density points sampled

density_ids = length(A)/temp_ids;

%Grab density matrix

density = A((1:density_ids),1);

%Grab temperature matrix

pressure = A(:,3);

%Reshape temperature matrix so it has one column for each temperature

%(isotherm), rather than just a single long column

pressure = reshape(pressure,[density_ids,temp_ids]);

%Differentiate

%dPdD = gradient(pressure(:,1)) / gradient(density);

[~,dPdD] = gradient(pressure, mean(diff(density)));

[~,ddPddD_grad] = gradient(dPdD, mean(diff(density)));

ddPddD_del2 = 4 *del2(pressure, mean(diff(density)));

subplot(1,2,1)

plot(density, ddPddD_grad)

grid on;

xlim([0.4 0.8])

xlabel('\rho (g/cm^3)');

ylabel('\partial^2p/\partial\rho^2')

subplot(1,2,2)

plot(density, ddPddD_del2)

grid on;

xlim([0.4 0.8])

xlabel('\rho (g/cm^3)');

ylabel('\partial^2p/\partial\rho^2')

temperature = 100:5:300;

density_spacing = density(2,1) - density(1,1);

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### Accepted Answer

Miriam
on 20 Nov 2018

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