Unable to convert expression containing symbolic variables into double array.
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I am following this algorithm (pic) and in Step 4, in the line "wij(i,2)=(1-lambda^2)*f(i*h)+(lambda^2/2)*(f((i+1)*h)+f((i-1)*h))+k*g(i*h);" I am getting the error "Unable to convert expression containing symbolic variables into double array. Apply 'subs' function first to substitute values for variables." I tried applying subs to f(i*h) and g(i*h), so it was wij(i,2)=(1-lambda^2)*(subs(f(x),x,(i*h)))+(lambda^2/2)*(subs(f(x),x,((i+1)*h)))+(subs(f(x),x,((i-1)*h)))+k*(subs(g(x),x,(i*h))); but I still get the same error. Please help
This is my whole program:
%Problem:
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=2:N
wij(1,j)=0; %wij(0,j)
wij(m,j)=0;
end
%STEP3
wij(1,1)=f(0); %wij(0,0)
wij(m,1)=f(l);
%STEP4
for i=2:m-1
wij(i,1)=subs(f(x),x,(i*h)); %wij(i,0)
wij(i,2)=(1-lambda^2)*(subs(f(x),x,(i*h)))+(lambda^2/2)*(subs(f(x),x,((i+1)*h)))+(subs(f(x),x,((i-1)*h)))+k*(subs(g(x),x,(i*h)));
end
%STEP5
for j=2:N-1
for i=2: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=1:N
t=j*k;
for i=1:m
x=i*h;
fprintf( '%.1f %.1f %.10f',x,t,wij(i,j))
end
end
Accepted Answer
%Problem:
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
wij = zeros(m,N,'sym');
for j=2:N
wij(1,j)=0; %wij(0,j)
wij(m,j)=0;
end
%STEP3
wij(1,1)=f(0); %wij(0,0)
wij(m,1)=f(l);
%STEP4
for i=2:m-1
wij(i,1)=subs(f(x),x,(i*h)); %wij(i,0)
wij(i,2)=(1-lambda^2)*(subs(f(x),x,(i*h)))+(lambda^2/2)*(subs(f(x),x,((i+1)*h)))+(subs(f(x),x,((i-1)*h)))+k*(subs(g(x),x,(i*h)));
end
%STEP5
for j=2:N-1
for i=2:m-1
wij(i,j+1)=2*(1-lambda^2)*wij(i,j)+lambda^2*(wij(i+1,j)+wij(i-1,j))-wij(i,j-1);
end
end
%STEP6
for j=1:N
t=j*k;
for i=1:m
x=i*h;
fprintf( '%.1f %.1f %s\n',x, t, char(vpa(wij(i,j),10)));
end
end
2 Comments
LightFury Yeji
on 7 Feb 2021
Walter Roberson
on 7 Feb 2021
%STEP6
stopping_loop = false;
for j=1:N
t=j*k;
for i=1:m
x=i*h;
if ~isempty(symvar(wij(i,j))
stopping_loop = true;
break;
end
fprintf( '%.1f %.1f %.10f\n',x, t, double(wij(i,j)));
end
if stopping_loop; break; end
end
More Answers (1)
toka hakim
on 21 May 2021
syms x;
f=cos(x)-x;
x1=0.5;
x2=pi/4;
for i=3:6
x(i)=x(i-1)-(f(x(i-1))*(x(i-1)-x(i-2)))/f(x(i-1)-f(x(i-2)));
vpa(x(i),10);
end
1 Comment
Walter Roberson
on 21 May 2021
It is not clear how this is an Answer to the question that was asked?
Categories
Find more on Conversion Between Symbolic and Numeric in Help Center and File Exchange
on 7 Feb 2021
on 21 May 2021
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