double integral problem pleas help

hello this is my loop for integration and asseble a matrix m but not works. what is my mistake ?

syms x %xi

syms y %eta

%

fun(1) = -.25.*(1-x).*(1-y).*(1 + x + y) ;

fun(2) = 0.5.*(1 - x.^2).*(1-y) ;

fun(3) = -.25*(1+x).*(1-y).*(1 - x + y) ;

fun(4) = 0.5.*(1+x).*(1 - y.^2) ;

fun(5) = -.25.*(1+x).*(1+y).*(1 - x - y) ;

fun(6) = 0.5.*(1 - x.^2).*(1+y) ;

fun(7) = -.25.*(1-x).*(1+y).*(1 + x - y) ;

fun(8) = 0.5.*(1-x).*(1 - y.^2) ;

m=zeros(8,8) ;

k=1 ;

for i=1:8

for j=1:8

a(k)=fun(i).*fun(j) ;

func=@(x,y) a(k);

l=integral2(func,-1,1,-1,1) ;

m(i,j)=m(i,j)+l ;

k=k+1 ;

end

end

[Sara Boznik]

Hi! Tell me if in this fun (n) you have to put for both x and y the same value, so I mean fun (1) where is x=1 and y=1?

Answer 1

[Star Strider]

The integral2 function is not appropriate for symbolic arguments.

Try this version of the loop instead:

m=zeros(8,8) ;
k=1 ;
 for i=1:8
     for j=1:8
         a(k)=fun(i).*fun(j) ;
         func=@(x,y) a(k);
         l=int(int(func,x,-1,1),y,-1,1) ;
         m(i,j)=m(i,j)+l ; 
         k=k+1 ;
     end
 end

The rest of the code is unchanged.

[Sara Boznik]

I get error with fun (1), I think there is something wrong.

[Star Strider]

It runs for me without error in R2020a, and with:

M = vpa(m,5)

produces:

M =
[  0.13333, -0.13333, 0.044444, -0.17778, 0.066667, -0.17778, 0.044444, -0.13333]
[ -0.13333,  0.71111, -0.13333,  0.44444, -0.17778,  0.35556, -0.17778,  0.44444]
[ 0.044444, -0.13333,  0.13333, -0.13333, 0.044444, -0.17778, 0.066667, -0.17778]
[ -0.17778,  0.44444, -0.13333,  0.71111, -0.13333,  0.44444, -0.17778,  0.35556]
[ 0.066667, -0.17778, 0.044444, -0.13333,  0.13333, -0.13333, 0.044444, -0.17778]
[ -0.17778,  0.35556, -0.17778,  0.44444, -0.13333,  0.71111, -0.13333,  0.44444]
[ 0.044444, -0.17778, 0.066667, -0.17778, 0.044444, -0.13333,  0.13333, -0.13333]
[ -0.13333,  0.44444, -0.17778,  0.35556, -0.17778,  0.44444, -0.13333,  0.71111]

Nothing appears to be wrong when I run it.