Unable to convert expression containing symbolic variables into double array.

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

Answer 1

[Walter Roberson]

%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

[LightFury Yeji]

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]

%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

Answer 2

[toka hakim]

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

[Walter Roberson]

It is not clear how this is an Answer to the question that was asked?