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Unable to convert expression containing symbolic variables into double array.

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LightFury Yeji
LightFury Yeji on 7 Feb 2021
Commented: Walter Roberson on 21 May 2021
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

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Accepted Answer

Walter Roberson
Walter Roberson on 7 Feb 2021
Ran in:
%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
0.1 0.1 0.0 0.2 0.1 0.5877852523 0.3 0.1 0.8090169944 0.4 0.1 0.9510565163 0.5 0.1 1.0 0.6 0.1 0.9510565163 0.7 0.1 0.8090169944 0.8 0.1 0.5877852523 0.9 0.1 0.3090169944 1.0 0.1 0.0 0.1 0.1 0.0 0.2 0.1 0.02938926261*cos(6.283185307*t) + 0.7135254916 0.3 0.1 0.04045084972*cos(6.283185307*t) + 1.06331351 0.4 0.1 0.04755282581*cos(6.283185307*t) + 1.309016994 0.5 0.1 0.05*cos(6.283185307*t) + 1.426584774 0.6 0.1 0.04755282581*cos(6.283185307*t) + 1.404508497 0.7 0.1 0.04045084972*cos(6.283185307*t) + 1.244949142 0.8 0.1 0.02938926261*cos(6.283185307*t) + 0.9635254916 0.9 0.1 0.01545084972*cos(6.283185307*t) + 0.5877852523 1.0 0.1 0.0 0.1 0.2 0.0 0.2 0.2 0.04045084972*cos(6.283185307*t) + 0.4755282581 0.3 0.2 0.07694208843*cos(6.283185307*t) + 1.213525492 0.4 0.2 0.09045084972*cos(6.283185307*t) + 1.538841769 0.5 0.2 0.09510565163*cos(6.283185307*t) + 1.713525492 0.6 0.2 0.09045084972*cos(6.283185307*t) + 1.720477401 0.7 0.2 0.07694208843*cos(6.283185307*t) + 1.559016994 0.8 0.2 0.05590169944*cos(6.283185307*t) + 1.244949142 0.9 0.2 0.02938926261*cos(6.283185307*t) + 0.6545084972 1.0 0.2 0.0 0.1 0.2 0.0 0.2 0.2 0.04755282581*cos(6.283185307*t) + 0.5 0.3 0.2 0.09045084972*cos(6.283185307*t) + 0.9510565163 0.4 0.2 0.1244949142*cos(6.283185307*t) + 1.618033989 0.5 0.2 0.1309016994*cos(6.283185307*t) + 1.832734395 0.6 0.2 0.1244949142*cos(6.283185307*t) + 1.868033989 0.7 0.2 0.1059016994*cos(6.283185307*t) + 1.720477401 0.8 0.2 0.07694208843*cos(6.283185307*t) + 1.25 0.9 0.2 0.04045084972*cos(6.283185307*t) + 0.6571638901 1.0 0.2 0.0 0.1 0.2 0.0 0.2 0.2 0.05*cos(6.283185307*t) + 0.4755282581 0.3 0.2 0.09510565163*cos(6.283185307*t) + 0.9045084972 0.4 0.2 0.1309016994*cos(6.283185307*t) + 1.244949142 0.5 0.2 0.1538841769*cos(6.283185307*t) + 1.772542486 0.6 0.2 0.1463525492*cos(6.283185307*t) + 1.832734395 0.7 0.2 0.1244949142*cos(6.283185307*t) + 1.559016994 0.8 0.2 0.09045084972*cos(6.283185307*t) + 1.132692148 0.9 0.2 0.04755282581*cos(6.283185307*t) + 0.5954915028 1.0 0.2 0.0 0.1 0.3 0.0 0.2 0.3 0.04755282581*cos(6.283185307*t) + 0.4045084972 0.3 0.3 0.09045084972*cos(6.283185307*t) + 0.7694208843 0.4 0.3 0.1244949142*cos(6.283185307*t) + 1.059016994 0.5 0.3 0.1463525492*cos(6.283185307*t) + 1.244949142 0.6 0.3 0.1538841769*cos(6.283185307*t) + 1.463525492 0.7 0.3 0.1309016994*cos(6.283185307*t) + 1.244949142 0.8 0.3 0.09510565163*cos(6.283185307*t) + 0.9045084972 0.9 0.3 0.05*cos(6.283185307*t) + 0.4755282581 1.0 0.3 0.0 0.1 0.4 0.0 0.2 0.4 0.04045084972*cos(6.283185307*t) + 0.2938926261 0.3 0.4 0.07694208843*cos(6.283185307*t) + 0.5590169944 0.4 0.4 0.1059016994*cos(6.283185307*t) + 0.7694208843 0.5 0.4 0.1244949142*cos(6.283185307*t) + 0.75 0.6 0.4 0.1309016994*cos(6.283185307*t) + 0.6571638901 0.7 0.4 0.1244949142*cos(6.283185307*t) + 0.8090169944 0.8 0.4 0.09045084972*cos(6.283185307*t) + 0.5877852523 0.9 0.4 0.04755282581*cos(6.283185307*t) + 0.3090169944 1.0 0.4 0.0 0.1 0.4 0.0 0.2 0.4 0.02938926261*cos(6.283185307*t) + 0.1545084972 0.3 0.4 0.05590169944*cos(6.283185307*t) + 0.2938926261 0.4 0.4 0.07694208843*cos(6.283185307*t) + 0.25 0.5 0.4 0.09045084972*cos(6.283185307*t) + 0.181635632 0.6 0.4 0.09510565163*cos(6.283185307*t) + 0.09549150281 0.7 0.4 0.09045084972*cos(6.283185307*t) 0.8 0.4 0.07694208843*cos(6.283185307*t) + 0.2135254916 0.9 0.4 0.04045084972*cos(6.283185307*t) + 0.1122569941 1.0 0.4 0.0 0.1 0.5 0.0 0.2 0.5 0.01545084972*cos(6.283185307*t) 0.3 0.5 0.02938926261*cos(6.283185307*t) - 0.1545084972 0.4 0.5 0.04045084972*cos(6.283185307*t) - 0.2938926261 0.5 0.5 0.04755282581*cos(6.283185307*t) - 0.4045084972 0.6 0.5 0.05*cos(6.283185307*t) - 0.4755282581 0.7 0.5 0.04755282581*cos(6.283185307*t) - 0.5 0.8 0.5 0.04045084972*cos(6.283185307*t) - 0.4755282581 0.9 0.5 0.02938926261*cos(6.283185307*t) - 0.09549150281 1.0 0.5 0.0 0.1 0.5 0.0 0.2 0.5 -0.3090169944 0.3 0.5 -0.5877852523 0.4 0.5 -0.8090169944 0.5 0.5 -0.9510565163 0.6 0.5 -1.0 0.7 0.5 -0.9510565163 0.8 0.5 -0.8090169944 0.9 0.5 -0.5877852523 1.0 0.5 0.0 0.1 0.6 0.0 0.2 0.6 - 0.01545084972*cos(6.283185307*t) - 0.5877852523 0.3 0.6 - 0.02938926261*cos(6.283185307*t) - 0.9635254916 0.4 0.6 - 0.04045084972*cos(6.283185307*t) - 1.244949142 0.5 0.6 - 0.04755282581*cos(6.283185307*t) - 1.404508497 0.6 0.6 - 0.05*cos(6.283185307*t) - 1.426584774 0.7 0.6 - 0.04755282581*cos(6.283185307*t) - 1.309016994 0.8 0.6 - 0.04045084972*cos(6.283185307*t) - 1.06331351 0.9 0.6 - 0.02938926261*cos(6.283185307*t) - 0.7135254916 1.0 0.6 0.0 0.1 0.6 0.0 0.2 0.6 - 0.02938926261*cos(6.283185307*t) - 0.6545084972 0.3 0.6 - 0.05590169944*cos(6.283185307*t) - 1.244949142 0.4 0.6 - 0.07694208843*cos(6.283185307*t) - 1.559016994 0.5 0.6 - 0.09045084972*cos(6.283185307*t) - 1.720477401 0.6 0.6 - 0.09510565163*cos(6.283185307*t) - 1.713525492 0.7 0.6 - 0.09045084972*cos(6.283185307*t) - 1.538841769 0.8 0.6 - 0.07694208843*cos(6.283185307*t) - 1.213525492 0.9 0.6 - 0.04045084972*cos(6.283185307*t) - 0.4755282581 1.0 0.6 0.0 0.1 0.7 0.0 0.2 0.7 - 0.04045084972*cos(6.283185307*t) - 0.6571638901 0.3 0.7 - 0.07694208843*cos(6.283185307*t) - 1.25 0.4 0.7 - 0.1059016994*cos(6.283185307*t) - 1.720477401 0.5 0.7 - 0.1244949142*cos(6.283185307*t) - 1.868033989 0.6 0.7 - 0.1309016994*cos(6.283185307*t) - 1.832734395 0.7 0.7 - 0.1244949142*cos(6.283185307*t) - 1.618033989 0.8 0.7 - 0.09045084972*cos(6.283185307*t) - 0.9510565163 0.9 0.7 - 0.04755282581*cos(6.283185307*t) - 0.5 1.0 0.7 0.0 0.1 0.7 0.0 0.2 0.7 - 0.04755282581*cos(6.283185307*t) - 0.5954915028 0.3 0.7 - 0.09045084972*cos(6.283185307*t) - 1.132692148 0.4 0.7 - 0.1244949142*cos(6.283185307*t) - 1.559016994 0.5 0.7 - 0.1463525492*cos(6.283185307*t) - 1.832734395 0.6 0.7 - 0.1538841769*cos(6.283185307*t) - 1.772542486 0.7 0.7 - 0.1309016994*cos(6.283185307*t) - 1.244949142 0.8 0.7 - 0.09510565163*cos(6.283185307*t) - 0.9045084972 0.9 0.7 - 0.05*cos(6.283185307*t) - 0.4755282581 1.0 0.7 0.0 0.1 0.8 0.0 0.2 0.8 - 0.05*cos(6.283185307*t) - 0.4755282581 0.3 0.8 - 0.09510565163*cos(6.283185307*t) - 0.9045084972 0.4 0.8 - 0.1309016994*cos(6.283185307*t) - 1.244949142 0.5 0.8 - 0.1538841769*cos(6.283185307*t) - 1.463525492 0.6 0.8 - 0.1463525492*cos(6.283185307*t) - 1.244949142 0.7 0.8 - 0.1244949142*cos(6.283185307*t) - 1.059016994 0.8 0.8 - 0.09045084972*cos(6.283185307*t) - 0.7694208843 0.9 0.8 - 0.04755282581*cos(6.283185307*t) - 0.4045084972 1.0 0.8 0.0 0.1 0.8 0.0 0.2 0.8 - 0.04755282581*cos(6.283185307*t) - 0.3090169944 0.3 0.8 - 0.09045084972*cos(6.283185307*t) - 0.5877852523 0.4 0.8 - 0.1244949142*cos(6.283185307*t) - 0.8090169944 0.5 0.8 - 0.1309016994*cos(6.283185307*t) - 0.6571638901 0.6 0.8 - 0.1244949142*cos(6.283185307*t) - 0.75 0.7 0.8 - 0.1059016994*cos(6.283185307*t) - 0.7694208843 0.8 0.8 - 0.07694208843*cos(6.283185307*t) - 0.5590169944 0.9 0.8 - 0.04045084972*cos(6.283185307*t) - 0.2938926261 1.0 0.8 0.0 0.1 0.9 0.0 0.2 0.9 - 0.04045084972*cos(6.283185307*t) - 0.1122569941 0.3 0.9 - 0.07694208843*cos(6.283185307*t) - 0.2135254916 0.4 0.9 -0.09045084972*cos(6.283185307*t) 0.5 0.9 - 0.09510565163*cos(6.283185307*t) - 0.09549150281 0.6 0.9 - 0.09045084972*cos(6.283185307*t) - 0.181635632 0.7 0.9 - 0.07694208843*cos(6.283185307*t) - 0.25 0.8 0.9 - 0.05590169944*cos(6.283185307*t) - 0.2938926261 0.9 0.9 - 0.02938926261*cos(6.283185307*t) - 0.1545084972 1.0 0.9 0.0 0.1 0.9 0.0 0.2 0.9 0.09549150281 - 0.02938926261*cos(6.283185307*t) 0.3 0.9 0.4755282581 - 0.04045084972*cos(6.283185307*t) 0.4 0.9 0.5 - 0.04755282581*cos(6.283185307*t) 0.5 0.9 0.4755282581 - 0.05*cos(6.283185307*t) 0.6 0.9 0.4045084972 - 0.04755282581*cos(6.283185307*t) 0.7 0.9 0.2938926261 - 0.04045084972*cos(6.283185307*t) 0.8 0.9 0.1545084972 - 0.02938926261*cos(6.283185307*t) 0.9 0.9 -0.01545084972*cos(6.283185307*t) 1.0 0.9 0.0 0.1 1.0 0.0 0.2 1.0 0.5877852523 0.3 1.0 0.8090169944 0.4 1.0 0.9510565163 0.5 1.0 1.0 0.6 1.0 0.9510565163 0.7 1.0 0.8090169944 0.8 1.0 0.5877852523 0.9 1.0 0.3090169944 1.0 1.0 0.0 0.1 1.0 0.0 0.2 1.0 0.02938926261*cos(6.283185307*t) + 0.7135254916 0.3 1.0 0.04045084972*cos(6.283185307*t) + 1.06331351 0.4 1.0 0.04755282581*cos(6.283185307*t) + 1.309016994 0.5 1.0 0.05*cos(6.283185307*t) + 1.426584774 0.6 1.0 0.04755282581*cos(6.283185307*t) + 1.404508497 0.7 1.0 0.04045084972*cos(6.283185307*t) + 1.244949142 0.8 1.0 0.02938926261*cos(6.283185307*t) + 0.9635254916 0.9 1.0 0.01545084972*cos(6.283185307*t) + 0.5877852523 1.0 1.0 0.0
  2 Comments
LightFury Yeji
LightFury Yeji on 7 Feb 2021
Thank you so much for this! Is there any way I can only display the first eleven lines of the answer?
0.1 0.1 0.0
0.2 0.1 0.5877852523
0.3 0.1 0.8090169944
0.4 0.1 0.9510565163
0.5 0.1 1.0
0.6 0.1 0.9510565163
0.7 0.1 0.8090169944
0.8 0.1 0.5877852523
0.9 0.1 0.3090169944
1.0 0.1 0.0
Walter Roberson
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

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More Answers (1)

toka hakim
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

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