I keep getting this error:

clear all
M=input('Enter M =')
N=input('Enter N=')
r=input('Enter r=')
f=input('Enter f=')
L=pi;
h=L/M;
%------&------------------------&------------------------------&-----------------*
%Ne kete program behet zgjidhja numerike e nje problemi diferencial valor
%me shuarje kufitare.Metoda e perdorur eshte ajo e tipit te
%karakteristikave .Ajo shfrytezon rrjetin specifik  te nyjeve qe gjenerojne
%kurbat karakterisitke te ekuacionit si dhe vecorite e kushteve
%fillestare-kufitare te problemit 

%-------&-----------------------&---------------------------------&--------------* 
for i=1:M+1

x(i,1)=i*h;
u(i,1)=sin(x(i,1));
xu(i,1)=cos(x(i,1));  %derivati ne lidhje me x;
tu(i,1)=cos(x(i,1)); %derivati ne lidhje me t;

end

     for j=1:N+1

           for i=2:M

            xu(x(i,j+1))=1/2*[cos(x(i,j))+cos(x(i-1,j))+cos(x(i,j))-cos(x(i-1,j))]+h/8*[r*(cos(x(i,j))-(1/f)*(cos(x(i,j))))-r*(cos(x(i-1,j))-(1/f)*(cos(x(i-1,j))))];

            tu(x(i,j+1))=1/2*[cos(x(i,j))-cos(x(i-1,j))+cos(x(i,j))+cos(x(i-1,j))]+h/8*[r*(cos(x(i,j))-(1/f)*(cos(x(i,j))))+2*(r*(cos(x(i,j+1))-(1/f)*(cos(x(i,j+1)))))+r*(cos(x(i-1,j))-(1/f)*(cos(x(i-1,j))))];

            u(x(i,j+1))=1/2*[sin(x(i-1,j))+sin(x(i,j))]+h/8*[cos(x(i-1,j))-cos(x(i,j))+cos(x(i-1,j))+2*cos(x(i,j+1))+cos(x(i,j))];
           end
     end

------------------------------------------------------------------------------

??? Index exceeds matrix dimensions.

Error in ==> MOC at 30
          xu(x(i,j+1))=1/2*[cos(x(i,j))+cos(x(i-1,j))+cos(x(i,j))-cos(x(i-1,j))]+h/8*[r*(cos(x(i,j))-(1/f)*(cos(x(i,j))))-r*(cos(x(i-1,j))-(1/f)*(cos(x(i-1,j))))];

Answer 1

[Walter Roberson]

You initialize x(:,1) but you use x(:,j) with j > 1

[Gentian Zavalani]

Could suggest me any solution please

[Walter Roberson]

You need to assign values to x(i,j) at some point, but I do not know where would be appropriate. My guess would be that it should be done before the "for j" loop, instead of only initializing x(i,1)