Program does not show the matrix

6 次查看（过去 30 天）
LightFury Yeji
LightFury Yeji 2021-1-27
评论： LightFury Yeji 2021-1-30
This program is made to approximate the solution to the Poisson equation. I have no errors with the equations, but it won't display the matrix and proceeds with displaying "End". Please help
a=0;
b=2;
c=0;
d=1;
m=5;
n=6;
N= 100;
TOL = 10^-4;
syms ga(y) gb(y) gc(x) gd(x) f(x,y);
f(x,y)=x*exp(y);
ga(y)=0;
gb(y)=2*exp(y);
gc(x)=x;
gd(x) =x*exp(1);
h=(b-a)/n;
k=(d-c)/m;
for i = 1:n-1
xi(i)=a+i*h;
end
for j = 1:m-1
yj(j)=c+j*k;
end
for i=1:n-1
for j=1:m-1
wij(i,j)=0;
end
end
lambda=h^2/k^2;
mu=2*(1+lambda);
l=1;
while l <= N
z=(-(h^2)*f(xi(1),yj(m-1))+ga(yj(m-1))+lambda*gd(xi(1))+lambda*wij(1,m-2)+wij(2,m-1))/mu;
NORM=abs(z-wij(1,m-1));
wij(1,m-1)=z;
for i=2:n-2
z = (-h^2*f(xi(i),yj(m-1))+lambda*gd(xi(i))+wij(i-1,m-1)+wij(i+1,m-1)+lambda*wij(i,m-2))/mu;
if abs(wij(i,m-1)-z)>NORM
NORM = abs(wij(i,m-1)-z);
end
wij(i,m-1) = z;
end
z=(-h^2*f(xi(n-1),yj(m-1))+gb(yj(m-1))+lambda*gd(xi(n-1))+wij(n-2,m-1)+lambda*wij(n-1,m-2))/mu;
if abs (wij(n-1,m-1)-z) > NORM
NORM = abs (wij(n-1,m-1)-z);
end
wij(n-1,m-1)=z;
for j=m-2:-1:2
z=(-(h^2)*f(xi(1),yj(j))+ga(yj(j))+lambda*wij(1,j+1)+lambda*wij(1,j-1)+wij(2,j))/mu;
if abs(wij(1,j)-z)>NORM
NORM = abs(wij(1,j)-z);
end
wij(i,j)=z;
for i=2:n-2
z=(-(h^2)*f(xi(i),yj(j))+wij(i-1,j)+lambda*wij(i,j+1)+wij(i+1,j)+lambda*wij(i,j-1))/mu;
if abs (wij(i,j)-z)>NORM
NORM=abs(wij(i,j)-z);
end
wij(i,j)=z;
end
z=(-h^2*f(xi(n-1),yj(j))+gb(yj(j))+wij(n-2,j)+lambda*wij(n-1,j+1)+lambda*wij(n-1,j-1))/mu;
if abs(wij(n-1,j)-z)>NORM
NORM=abs(wij(n-1,j)-z);
end
wij(n-1,j)=z;
end
z = (-h^2*f(xi(1),yj(1))+ga(yj(1))+lambda*gc(xi(1))+lambda*wij(1,2)+wij(2,1))/mu;
if abs(wij(1,1)-z) > NORM
NORM = abs(wij(1,1)-z);
end
wij(1,1) = z;
for i = 2:n-2
z = (-h^2*f(xi(i),yj(1))+lambda*gc(xi(i))+wij(i-1,1)+lambda*wij(i,2)+wij(i+1,1))/mu;
if abs(wij(i,1)-z)>NORM
NORM = abs(wij(i,1)-z);
end
wij(i,1) = z;
end
z=(-h^2*f(xi(n-1),yj(1))+gb(yj(1))+lambda*gc(xi(n-1))+wij(n-2,1)+lambda*wij(n-1,2))/mu;
if abs (wij(n-1,1)-z) > NORM
NORM= abs(wij(n-1,1)-z) ;
end
wij(n-1,1)=z;
if NORM<= TOL
for i=1:n-1
for j=1:m-1
MATRIX(i)=[xi(i) yj(j) wij(i,j)];
end
end
display(MATRIX)
end
l=l+1;
end
display("End")
  2 个评论
Rik
Rik 2021-1-29
I restored the edit from Google cache.
@LightFury Yeji it is very rude to edit away major parts of your question after receiving an answer. Please don't do it again.
LightFury Yeji
LightFury Yeji 2021-1-30
Hi! Sorry for that, I did it because the answer is not correct and I thought it would confuse others. I would not do it again.

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回答（1 个）

Walter Roberson
Walter Roberson 2021-1-27
Ran in:
a=0;
b=2;
c=0;
d=1;
m=5;
n=6;
N= 100;
TOL = 10^-4;
syms ga(y) gb(y) gc(x) gd(x) f(x,y);
f(x,y)=x*exp(y);
ga(y)=0;
gb(y)=2*exp(y);
gc(x)=x;
gd(x) =x*exp(1);
h=(b-a)/n;
k=(d-c)/m;
for i = 1:n-1
xi(i)=a+i*h;
end
for j = 1:m-1
yj(j)=c+j*k;
end
for i=1:n-1
for j=1:m-1
wij(i,j)=0;
end
end
lambda=h^2/k^2;
mu=2*(1+lambda);
l=1;
found = 0;
while l <= N
if found > 0
fprintf('solution was already found at iteration #%d, why did we start iteration %#d\n', found, l);
end
z=(-(h^2)*f(xi(1),yj(m-1))+ga(yj(m-1))+lambda*gd(xi(1))+lambda*wij(1,m-2)+wij(2,m-1))/mu;
NORM=abs(z-wij(1,m-1));
wij(1,m-1)=z;
for i=2:n-2
z = (-h^2*f(xi(i),yj(m-1))+lambda*gd(xi(i))+wij(i-1,m-1)+wij(i+1,m-1)+lambda*wij(i,m-2))/mu;
if abs(wij(i,m-1)-z)>NORM
NORM = abs(wij(i,m-1)-z);
end
wij(i,m-1) = z;
end
z=(-h^2*f(xi(n-1),yj(m-1))+gb(yj(m-1))+lambda*gd(xi(n-1))+wij(n-2,m-1)+lambda*wij(n-1,m-2))/mu;
if abs (wij(n-1,m-1)-z) > NORM
NORM = abs (wij(n-1,m-1)-z);
end
wij(n-1,m-1)=z;
for j=m-2:-1:2
z=(-(h^2)*f(xi(1),yj(j))+ga(yj(j))+lambda*wij(1,j+1)+lambda*wij(1,j-1)+wij(2,j))/mu;
if abs(wij(1,j)-z)>NORM
NORM = abs(wij(1,j)-z);
end
wij(i,j)=z;
for i=2:n-2
z=(-(h^2)*f(xi(i),yj(j))+wij(i-1,j)+lambda*wij(i,j+1)+wij(i+1,j)+lambda*wij(i,j-1))/mu;
if abs (wij(i,j)-z)>NORM
NORM=abs(wij(i,j)-z);
end
wij(i,j)=z;
end
z=(-h^2*f(xi(n-1),yj(j))+gb(yj(j))+wij(n-2,j)+lambda*wij(n-1,j+1)+lambda*wij(n-1,j-1))/mu;
if abs(wij(n-1,j)-z)>NORM
NORM=abs(wij(n-1,j)-z);
end
wij(n-1,j)=z;
end
z = (-h^2*f(xi(1),yj(1))+ga(yj(1))+lambda*gc(xi(1))+lambda*wij(1,2)+wij(2,1))/mu;
if abs(wij(1,1)-z) > NORM
NORM = abs(wij(1,1)-z);
end
wij(1,1) = z;
for i = 2:n-2
z = (-h^2*f(xi(i),yj(1))+lambda*gc(xi(i))+wij(i-1,1)+lambda*wij(i,2)+wij(i+1,1))/mu;
if abs(wij(i,1)-z)>NORM
NORM = abs(wij(i,1)-z);
end
wij(i,1) = z;
end
z=(-h^2*f(xi(n-1),yj(1))+gb(yj(1))+lambda*gc(xi(n-1))+wij(n-2,1)+lambda*wij(n-1,2))/mu;
if abs (wij(n-1,1)-z) > NORM
NORM= abs(wij(n-1,1)-z) ;
end
wij(n-1,1)=z;
if NORM<= TOL
for i=1:n-1
for j=1:m-1
MATRIX(i)=[xi(i) yj(j) wij(i,j)];
end
end
display(MATRIX)
found = l;
end
l=l+1;
end
display("End")
"End"
if found == 0
fprintf('Solution was never found, ran out of iterations\n');
else
fprintf('Solution was found at iteration #%d\n', found);
end
Solution was never found, ran out of iterations
  1 个评论
LightFury Yeji
LightFury Yeji 2021-1-30
I'm sorry, this program has an expected output -- solution should be found.

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