Error - Array indices must be positive integers or logical values

I am trying to solve a wave equation of the form d2u/dt2-a2*d2u/dx2=0 and have the following code:

xstep = 0.1;
tstep = 0.05; 
xstep2 = xstep*xstep;
tstep2 = tstep*tstep;
alpha = 2; 
alpha2 = alpha*alpha;
lambda2 = alpha2*tstep2/xstep2;

xdomain = [0 1]; 
tdomain = [0 1];

nx = round((xdomain(2)-xdomain(1))/xstep);
nt = round((tdomain(2)-tdomain(1))/tstep);

u = zeros(nx+1,nx+1); % solutions 
ustar = zeros(nx+1,1); % predictor step solution 
dxdt0 = zeros(nx+1,1); % predictor step solution 

%% initial condition 
for i=1:nx+1 
    i = 0;
    xi = (i-1)*xstep;
    if(xi>=0 && xi<=1)
    u(i,1) = sin(2*pi*xi); % initial condition , xt0(i)
    dxdt0(i) = alpha*pi*sin(2*pi*xi);
    u(i,2) = u(i,1) + dxdt0(i)*tstep; % using first order term for step 1 solution, xold(i), sol at tstep k
   %u(i,2) = u(i,2) - 100*pi*pi*cos((xi-0.4)*10*pi)*tstep2*alpha2; % 2nd order correction 
end 
end
%% create dynamic plot 
close all
x=linspace(xdomain(1),xdomain(2),nx+1);
h1=plot(x,xt0(:,t),'linewidth',2);
hold on;
h2=plot(x,xnew(:,t),'linewidth',2);
legend('Initital','Final');
xlabel('x [m]');
ylabel('Displacement [m]');
axis([0 1 -1 1]);
set(gca,'FontSize',16);

%% loop for time to obtain solution 
for k=2:nt % loop for time t
    time = k*tstep;
    for i=1:nx+1 % loop for x
        % Use periodic boundary condition, u(nx+1)=u(1)
        if(i==1) % the left boundary 
            u(i,k+1) = 2*(1-lambda2)*u(i,k) + lambda2*(u(i+1,k)+u(nx+1,k)) - u(i,k-1); 
        elseif(i==nx+1) % the right boundary
            u(i,k+1) = 2*(1-lambda2)*u(i,k) + lambda2*(u(1,k)+u(i-1,k)) - u(i,k-1);
        else % the interior node 
            u(i,k+1) = 2*(1-lambda2)*u(i,k) + lambda2*(u(i+1,k)+u(i-1,k)) - u(i,k-1);
        end 
    end 

I get an error at line 38 (x, xt0(:,t)) that the "Index in position 2 is invalid. Array indices must be positive integers or logical values." I believe this is related to the for loop of the initial condition, but I am not entirely sure what to change to fix the problem.

Answer 1

[Steven Lord]

Looking at a section of your code:

i = 0;
xi = (i-1)*xstep;
if(xi>=0 && xi<=1)
u(i,1) = sin(2*pi*xi); % initial condition , xt0(i)

There's no such thing as row 0 in a numeric array in MATLAB. The first row is row 1.

You're trying to assign to the element in the first column of row 0 on the last line of that section of code I copied.

[Matlab12345]

In that case, how would I assign the initial condition to u(i, 1)? If I set i = 1, I am told that "Array indices must be positive integers or logical values."