index must be positive integer or logical

I am using an explicit/implicit scheme for Gravity waves in one dimension and I'm using the following code.

ntot = 100;

jmax = 100;

j = 50;

h=10; dx = 1000; dt = 0.5;

a = (dt*h)/dx;

for j = 1:((n+1)) %Initial conditions

U(:,1)=0;

U(jmax/2,1) =100;

end

for n=1:ntot+1 %Boundary conditions

U(1,n) = 1;

U(n+1,n) = 0;

end

   for n = 1:ntot;
   for j = 1:jmax-1;

   N(j,n+1) = N(j,n)-a*(U(j+1/2,n)-U(j-1/2,n));

U(j+1/2,n) =U(j+1/2,n+1) - B*(N(j,n+1)-N(j+1,n+1));

end
end

hold on
 plot(N(:,n+1));
 plot (U(:,n));

However, when running it, an error "Attempted to access U(1.5,1); index must be a positive integer or logical." is being displayed. I understand why it is displaying such error (because j is located in the middle of each cell i.e. j is found at 0.5, 1.5, 2.5 etc...and matlab does not read such index. Is there a way how I can solve this problem please. Thanks

[Jan]

Please use the "{} Code" button to format your code. Currently it is hard to read.

Answer 1

[KSSV]

If you have a array/ matrix, the indices (i,j) must be integers. They cannot be fractions, zeros or negatives. You are accessing U(1.5,1). It is not allowed.

[MF]

Yes I know that, but how can I modify my code so that it reads j (which falls in the middle of n) since j is a disturbance in the middle of the domain..

Answer 2

[Jan]

The intention of your code is not clear. E.g. this is meaningless:

for j = 1:((n+1)) %Initial conditions
  U(:,1)      = 0;
  U(jmax/2,1) = 100;
end

The body of the loop does not depend on the loop counter j, such that you set the the elements n times to the same value. Why?

It is hard to suggest how to solve the problem of the non-integer indices, because the code does not contain any comments which explain the purpose. All we see is a failing code, so how could we fix it? Perhaps you should simply multiply all indices by 2. Or you could replace U(1.5) by (U(1)+U(2))/2, if this satisfies your needs.

[MF]

Ok, it looks like I didn't explained properly.

I've attached the equations I' working on. After arranging them I got these:

N(j,n+1) = N(j,n)-a*(U(j+1/2,n)-U(j-1/2,n)); (a = dt*/dx)

U(j+1/2,n) =U(j+1/2,n+1) - B*(N(j,n+1)-N(j+1,n+1)); (B = dt*g/dx).

Then I had to implement an explicit/implicit scheme and initialize the water level (i.e. j = 50) with an initial disturbance in the middle of the domain.

ntot = 100; %number of time steps

jmax = 100; %size of domain

j = 50; %initial perturbation

h=10; dx = 1000; dt = 0.5;

Since j in the equations (as attached in the image) contains a 1/2, I have no idea how I can solve it. Hope I explained it better now. Thanks

[Torsten]

I don't understand your problem.

Just save the values you would have stored in U(j+1/2,n) now in U(j+1,n) (i.e. shift the j-index by 1/2 to the right).

Best wishes

Torsten.

Answer 3

[Image Analyst]

There is a FAQ on that that explains it pretty well: http://matlab.wikia.com/wiki/FAQ#How_do_I_fix_the_error_.22Subscript_indices_must_either_be_real_positive_integers_or_logicals..22.3F