Index in position 1 is invalid but I need w(0,j), w(0,0), and w(m,0)

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I am following an algorithm for wave equations (shown on the pic). I get the error "Index in position 1 is invalid. Array indices must be positive integers or logical values." What do I do, if w(0,j), w(0,0), and w(m,0) are needed? Also, in this line "wij(i,1)=(1-lambda^2)*f(i*h)+(lambda^2/2)*(f((i+1)*h)+f((i-1)*h))+k*g(i*h);" i get the error "Unable to convert expression containing symbolic variables into double array." Help would be very much appreciated, thanks.
This is my program:
%STEP0
l=1; %endpoint
T=1; %maximum time
alpha = 2; %constant
m=10;
N=20;
syms f(x) g(x,t)
f(x)=sin(pi*x);
g(x)=(sin(pi*x))*(cos(2*pi*t));
%STEP1
h=l/m;
k=T/N;
lambda=k*alpha/h;
%STEP2
for j=1:N
wij(0,j)=0;
wij(m,j)=0;
end
%STEP3
wi(0,0)=f(0);
wi(m,0)=f(l);
%STEP4
for i=1:m-1
wij(i,0)=f(i*h);
wij(i,1)=(1-lambda^2)*f(i*h)+(lambda^2/2)*(f((i+1)*h)+f((i-1)*h))+k*g(i*h);
end
%STEP5
for j=1:N-1
for i=1:m-1
wij(i,j+1)=2*(1-lambda^2)*w(i,j)+lambda^2*(wij(i+1,j)+wij(i-1,j))-wij(i,j-1);
end
end
%STEP6
for j=0:N
t=j*k;
for i=0:m
x-i*h;
fprintf( '%.1f %.1f %.10f',x,t,wij(i,j))
end
end

Accepted Answer

Jos Jordan
Jos Jordan on 6 Feb 2021
Edited: Jos Jordan on 6 Feb 2021
I'm pretty sure the answer here is that unlike most other languages, MATLAB starts indexing at 1, not 0. So for example in the code you wrote:
%STEP 2
for j=1:N
wij(1,j)=0;
wij(m,j)=0;
end
would give the desired result - you would then have to change the others to have an index of 1 instead of 0.
  3 Comments
Jos Jordan
Jos Jordan on 6 Feb 2021
I think so - in the problem everything is indexed from 0, so you want to index from 1 - if you think about what you're doing carefully you should be able to see which parts you need to add 1 to.
In Step 4 you are doing:
which in your code is:
for i=1:m-1
wij(i,1)=f(i*h);
wij(i,2)=(1-lambda^2)*f(i*h)+(lambda^2/2)*(f((i+1)*h)+f((i-1)*h))+k*g(i*h);
end
as you starting the index of the second subscript at 1 as oppose to 2.
By the looks of it, you should also set
for i=2:m
wij(i,1)=f(i*h);
wij(i,2)=(1-lambda^2)*f(i*h)+(lambda^2/2)*(f((i+1)*h)+f((i-1)*h))+k*g(i*h);
end
changing the value of i you are looping over, as again you are adding one to the index there as in the problem it states:
so you want to be iterating from the second index of the i in your code. If you cange the rest of it - it should work, I believe. If not I'll test it and see.

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