%first and second derivative
df=diff(M1(j+1),t);
You have that line before your for j loop, so at that point j is its default value, sqrt(-1)
M1=zeros(length(t)+1,1); %empty array for M1
M1 is a numeric array
df=diff(M1(j+1),t);
M1(j+1) [with valid scalar j index] would be a scalar numeric value. diff() applied to numeric values is numeric differences. diff(X,N) is X(2:end)-X(1:end-1), repeated N times -- which requires that the second parameter is a positive integer numeric scalar. But...
t=0:dt:360; %time span
it is non-scalar, non-positive, and not integer.
There are two major functions named diff . The one that applies to most data types is what I mentioned above, X(2:end)-X(1:end-1) . There is also diff symbolic derivative. Symbolic derivative can work in two modes:
- if the first parameter is of data type sym, symfun, or symmatrix, then it is an expression whose derivative is to be taken, and the remaining parameters describe which variable to take the derivative with respect to, and how many derivatives to take;
- if the first parameter to the symbolic diff function is numeric and the second parameter is symbolic variable, then the numeric variable is converted to symbolic equivalent and the derivative is taken with respect to the variable... but the symbolic equivalent of a numeric variable is of course constant, and the derivative of a constant with respect to a variable is 0. So in this case, diff(Numeric_expression, symbolic_variable) would end up returning zeros the same size as the Numeric_expression
You, though, are trying to use diff() with numeric first parameter and numeric second parameter, so you are not invoking the symbolic derivative function at all.
What should you do? Well, you should perhaps create your M* matrixes over time (recording the matrix at each time step) and then call gradient to estimate the numeric gradient.
But it depends... do you want to take the derivative with respect to time, like your code suggests... or do you want to take the derivative with respect to space?
