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
