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ghw_nit

Ìú¸Ëľ³æ (ÕýʽдÊÖ)


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feval(f,(1:n-1)*h,(1:n-1)*h)
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ghw_nit

Ìú¸Ëľ³æ (ÕýʽдÊÖ)


fµÄmº¯ÊýÎÒÊÔ×ÅдÁ˺ü¸¸ö¶¼²»ÄÜͨ¹ý£¬ÄÄλ´óÏÀ¸øÑÝʾһÏÂÈçºÎʹÓã¬Íò·Ö¸Ðл
2Â¥2011-01-07 20:04:38
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ÒýÓûØÌû:
Originally posted by ghw_nit at 2011-01-07 20:04:38:
fµÄmº¯ÊýÎÒÊÔ×ÅдÁ˺ü¸¸ö¶¼²»ÄÜͨ¹ý£¬ÄÄλ´óÏÀ¸øÑÝʾһÏÂÈçºÎʹÓã¬Íò·Ö¸Ðл

°ïÖúÖÐÓÐʵÀý£¬ÕÒÀ´¿´¿´¾ÍÖªµÀÁË¡£
3Â¥2011-01-07 21:47:10
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ghw_nit

Ìú¸Ëľ³æ (ÕýʽдÊÖ)


ʵÀýÒѾ­¿´¹ýÁË£¬¾ÍÊǰѷ½³ÌµÄÓÒ±ßд³ÉÒ»¸ömÎļþ£¬
function f=f(x,y)
f=-2*pi^2*sin(pi*x)*sin(pi*y);
µ÷ÊÔʱ²»ÄÜͨ¹ý
4Â¥2011-01-08 10:12:37
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¡ï ¡ï
robert2020(½ð±Ò+2):ÐÁ¿àÁË£¡ 2011-01-11 11:28:07
ÒýÓûØÌû:
Originally posted by ghw_nit at 2011-01-08 10:12:37:
ʵÀýÒѾ­¿´¹ýÁË£¬¾ÍÊǰѷ½³ÌµÄÓÒ±ßд³ÉÒ»¸ömÎļþ£¬
function f=f(x,y)
f=-2*pi^2*sin(pi*x)*sin(pi*y);
µ÷ÊÔʱ²»ÄÜͨ¹ý

ÄãÊÇÔõÑùµ÷ÓõÄÄØ£¿¿ÉÄÜÊÇÄãµ÷Óõĸñʽ²»¶Ô°É£¬´íÎóÌáʾÊÇÊ²Ã´ÄØ£¿

fevalÓÐÁ½ÖÖÓ÷¨£º
[y1, y2, ...] = feval(fhandle, x1, ..., xn)£» % Óú¯Êý¾ä±ú
[y1, y2, ...] = feval(function, x1, ..., xn)£» % Ö±½ÓÓú¯ÊýÃû

¶ÔÄãµÄº¯Êý£¬Óú¯Êý¾ä±úµÄ»°£º
CODE:
fhandle = @f;
feval( fhandle, 0.1, 0.1 )

Óú¯ÊýÃû£º
CODE:
feval( 'f', 0.1, 0.1 )

5Â¥2011-01-08 10:28:14
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ghw_nit

Ìú¸Ëľ³æ (ÕýʽдÊÖ)


>> Poisson('f','g',16,1e-8,10000)
Warning: Could not find an exact (case-sensitive) match for 'Poisson'.
C:\Documents and Settings\lenovo\My Documents\MATLAB\poisson.m is a case-insensitive match and will be used
instead.
You can improve the performance of your code by using exact
name matches and we therefore recommend that you update your
usage accordingly. Alternatively, you can disable this warning using
warning('off','MATLAB:dispatcher:InexactCaseMatch').
This warning will become an error in future releases.
??? Error using ==> mtimes
Inner matrix dimensions must agree.

Error in ==> f at 2
f=-2*pi^2*sin(pi*x)*sin(pi*y);
Error in ==> poisson at 13
Fr(2:n,2:n)=h^2*feval(f,(1:n-1)*h,(1:n-1)*h);
´íÎóµÄÌáʾ
6Â¥2011-01-08 10:51:59
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû
ghw_nit(½ð±Ò+20):лл°æÖ÷ 2011-01-08 11:08:17
ÒýÓûØÌû:
Originally posted by ghw_nit at 2011-01-08 10:51:59:
>> Poisson('f','g',16,1e-8,10000)
Warning: Could not find an exact (case-sensitive) match for 'Poisson'.
C:\Documents and Settings\lenovo\My Documents\MATLAB\poisson.m is a case-insensitive ...

PoissonÊÇʲô¶«¶«£¬Äã×Ô¼ºÐ´µÄº¯ÊýÂð£¿Â·¾¶²»¶Ô¡£

ÁíÍâÄã´úÈëµÄx£¬y·Ö±ðΪ(1:n-1)*h£¬º¯ÊýÖÐf=-2*pi^2*sin(pi*x)*sin(pi*y)ÕâÑùдÊDz»¶ÔµÄ¡£
CODE:
f=-2 * pi ^2 * sin( pi * x ) .* sin( pi * y );

[ Last edited by xiegangmai on 2011-1-8 at 10:59 ]
7Â¥2011-01-08 10:57:32
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

ghw_nit

Ìú¸Ëľ³æ (ÕýʽдÊÖ)


ÏÖÔڵĴíÎóÊÇÕâÑùµÄ£¬
??? Subscripted assignment dimension mismatch.

Error in ==> poisson at 13
Fr(2:n,2:n)=h^2*feval(f,(1:n-1)*h,(1:n-1)*h);
poissonÊÇÒ»¸öº¯Êý
8Â¥2011-01-08 11:04:41
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

ghw_nit

Ìú¸Ëľ³æ (ÕýʽдÊÖ)


function U=poisson(f,g,n,tol,max_it)
if nargin<5
    max_it=10000
end
if nargin<4
    tol=1e-5
end

n1=n+1;
h=1/n;
toln=(h^2)*tol;
Fr=zeros(n,n);
Fr(2:n,2:n)=h^2*feval(f,(1:n-1)*h,(1:n-1)*h);

U=zeros(n1,n1);
U(1,1:n1)=feval(g,0,(0:n)*h);
U(n1,1:n1)=feval(g,1,(0:n)*h);
U(1:n1,1)=feval(g,(0:n)*h,0);
U(1:n1,n1)=feval(g,(0:n)*h,1);

rel_err=1;
itnum=0;
while((rel_err>toln)&(itnum<=max_it))
    err=0;
    umax=0;
    for j=2:n
        for i=2:n
            temp=(U(i+1,j)+U(i-1,j)+U(i,j+1)+U(i,j-1))/4-Fr(i,j);
            dif=abs(temp-u(i,j));
            if(err<=diff)
                err=dif;
            end
            U(i,j)=temp;
            temp=abs(temp);
            if(umax<=temp)
                umax=temp;
            end
        end
    end
    itnum=itnum+1;
    rel_err=err/umax;
end

%X=(0:h,:n*h)';
%Y=X;
%surf(X,Y,U')
%xlabel('x-axis')
%ylabel('y-axis')
%zlabel('the numerical solution')
%title('Plot of the mumerical solution')
X=(0:h:n*h)';Y=X;
subplot(1,2,1)
surf(X,Y,U')
xlabel('x-axis')
ylabel('y-axis')
zlabel('The numerical solution')
s1=springtf('h=6.4f',h)
title(s1)
hold on

Err=sin(pi*X)*sin(pi*Y')-U;
subplot(1,2,2)
surf(X,Y,Err')
9Â¥2011-01-08 11:05:13
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

ghw_nit

Ìú¸Ëľ³æ (ÕýʽдÊÖ)


ÕâÊÇÊéÖеijÌÐò£¬Çó½â²´ËÉ·½³ÌµÄ³ÌÐò
10Â¥2011-01-08 11:06:14
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ghw_nit

Ìú¸Ëľ³æ (ÕýʽдÊÖ)


ÎÒÏëµ÷ÊÔһϣ¬°´×ÅÊéÖеijÌÐò¾Í³öÏÖÁËÉÏÊöµÄÇé¿ö
11Â¥2011-01-08 11:06:47
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ghw_nit

Ìú¸Ëľ³æ (ÕýʽдÊÖ)


f´ú±í²´ËÉ·½³ÌÖеĺ¯Êý£¬gÊDZ߽çÌõ¼þ
12Â¥2011-01-08 11:09:33
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû
ÒýÓûØÌû:
Originally posted by ghw_nit at 2011-01-08 11:09:33:
f´ú±í²´ËÉ·½³ÌÖеĺ¯Êý£¬gÊDZ߽çÌõ¼þ

ÄãµÄ±ß½çº¯ÊýÄØ£¿
13Â¥2011-01-08 11:34:09
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ghw_nit

Ìú¸Ëľ³æ (ÕýʽдÊÖ)


±ß½çº¯ÊýÊÇ0
14Â¥2011-01-08 11:48:22
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ghw_nit

Ìú¸Ëľ³æ (ÕýʽдÊÖ)


Çó½âµÄ·¶Î§Êǵ¥Î»µÄÕý·½ÐΣ¬±ß½çÉϵĺ¯ÊýÖµ¶¼ÊÇ0
15Â¥2011-01-08 11:53:22
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû
¡ï ¡ï ¡ï ¡ï ¡ï ¡ï
Сľ³æ(½ð±Ò+0.5):¸ø¸öºì°ü£¬Ð»Ð»»ØÌû½»Á÷
robert2020(½ð±Ò+5):ÐÁ¿àÁË£¡ 2011-01-11 11:28:48
ÒýÓûØÌû:
Originally posted by ghw_nit at 2011-01-07 19:38:24:
ÏÖÔÚÔÚ¿´¡¶ÊýÖµ·ÖÎöµ¼ÂÛ¡·º«Î¼ÃôÒ룬379Ò³ÖеıßÖµÎÊÌ⣬

ÔÚ¶ÔÕâ¸öƫ΢·Ö·½³ÌµÄÇó½â¹ý³ÌÖÐÓõ½Ò»ÌõÓï¾ä
feval(f,(1:n-1)*h,(1:n-1)*h)
×¢ÊÍÖÐ˵Ã÷f·½³ÌµÄÓұߵĺ¯ÊýÖµ£¬ÎÒ²»ÖªµÀÈçºÎдÕâ¸öfµÄmº¯Êý£¬ÓÐÈË¿É ...

´ó¸ÅÐÞ¸ÄÁËһϣ¬²»ÖªµÀ½á¹û¶Ô²»¶Ô£¬×Ô¼ºÑé֤һϡ£
´ýÇó½â·½³Ìº¯Êý£º
CODE:
function ff = f( x, y )
ff = -2 * pi ^ 2 * sin( pi * x ) * sin( pi * y' );

±ß½çÌõ¼þ£º
CODE:
function ff = g( x, y )
ff = 0;

Poissonº¯Êý£º
CODE:
function U = poisson( f, g, n, tol, max_it )
if nargin < 5
    max_it = 10000;
end
if nargin < 4
    tol = 1e-5;
end

n1 = n + 1;
h = 1 / n;
toln = ( h ^ 2 ) * tol;
Fr = zeros( n, n );
Fr( 2 : n, 2 : n ) = h ^ 2 * feval( f, ( 1 : n - 1 ) * h, ( 1 : n - 1 ) * h );

U = zeros( n1, n1 );
U( 1, 1 : n1 ) = feval( g, 0, ( 0 : n ) * h );
U( n1, 1 : n1 ) = feval( g, 1, ( 0 : n ) * h );
U( 1 : n1, 1 ) = feval( g, ( 0 : n ) * h, 0 );
U( 1 : n1, n1 ) = feval( g, ( 0 : n ) * h, 1 );

rel_err = 1;
itnum = 0;
while( ( rel_err > toln ) && ( itnum <= max_it ) )
    err = 0;
    umax = 0;
    for j = 2 : n
        for i = 2 : n
            temp = ( U( i + 1, j ) + U( i - 1, j ) + U( i, j + 1 ) + U( i, j - 1 ) ) / 4 - Fr( i, j );
            diff = abs( temp - U( i, j ) );
            if ( err <= diff )
                err = diff;
            end
            U( i, j ) = temp;
            temp = abs( temp );
            if( umax <= temp )
                umax = temp;
            end
        end
    end
    itnum = itnum + 1;
    rel_err = err / umax;
end

X = ( 0 : h : n * h )';
Y = X;
subplot( 1, 2, 1 )
surf( X, Y, U' )
xlabel( 'x-axis' )
ylabel( 'y-axis' )
zlabel( 'The numerical solution' )

Err = sin( pi * X ) * sin( pi * Y' ) - U;
subplot( 1, 2, 2 )
surf( X, Y, Err' )

ÔÚÃüÁî´°¿ÚÊäÈ룺
CODE:
ff = @f;
gg = @g;
n = 20;
u = poisson( ff, gg, n );

µÃµ½µÄ½á¹û£º
16Â¥2011-01-08 12:03:07
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ghw_nit

Ìú¸Ëľ³æ (ÕýʽдÊÖ)


ÒѾ­µ÷ÊÔͨ¹ýÁË£¬Ð»Ð»°æÖ÷
17Â¥2011-01-08 13:37:10
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû
ÒýÓûØÌû:
Originally posted by ghw_nit at 2011-01-08 13:37:10:
ÒѾ­µ÷ÊÔͨ¹ýÁË£¬Ð»Ð»°æÖ÷

ÊDz»ÊÇÎó²îÌ«´óÁË£¿
18Â¥2011-01-08 14:13:18
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

ghw_nit

Ìú¸Ëľ³æ (ÕýʽдÊÖ)


ÄܰïÎÒ½âÊÍһϣ¬
ff = -2 * pi ^ 2 * sin( pi * x ) * sin( pi * y' )
yΪʲôһ¶¨ÒªÊÇתÖÃÄØ£¿
19Â¥2011-01-08 14:32:43
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû
¡ï
Сľ³æ(½ð±Ò+0.5):¸ø¸öºì°ü£¬Ð»Ð»»ØÌû½»Á÷
ÒýÓûØÌû:
Originally posted by ghw_nit at 2011-01-08 14:32:43:
ÄܰïÎÒ½âÊÍһϣ¬
ff = -2 * pi ^ 2 * sin( pi * x ) * sin( pi * y' )
yΪʲôһ¶¨ÒªÊÇתÖÃÄØ£¿

²»ºÃÒâ˼£¬¸ã´íÁË£¬ÕýÈ·µÄÓ¦¸ÃÊÇ£º
CODE:
ff = -2 * pi ^ 2 * sin( pi * x' ) * sin( pi * y );

Äã´úÈëµÄxÒ²y·Ö±ðΪһ¸öÐÐÏòÁ¿£¬°ÑxתÖÃһϣ¬ÔÙÏà³ËµÃµ½µÄ²ÅÊÇÐèÒªµÄ¾ØÕó¡£
20Â¥2011-01-08 15:21:26
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû
Ïà¹Ø°æ¿éÌø×ª ÎÒÒª¶©ÔÄÂ¥Ö÷ ghw_nit µÄÖ÷Ìâ¸üÐÂ
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[¿¼ÑÐ] 348Çóµ÷¼Á +4 СÀÁ³æ²»ÀÁÁË 2026-03-27 5/250 2026-03-27 12:47 by ¹û¹ûÂèßä
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