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crackpotop

Òø³æ (СÓÐÃûÆø)

[ÇóÖú] matlab Çó½â»ý·ÖÎÊÌâ

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matlab Çó½â»ý·ÖÎÊÌâ
²¢×÷³ö»ý·Ö½á¹ûµÄ·ùÖµÓë±äÁ¿aµÄͼÏñ£¬matlab³ÌÐòÈçÏ£º

b=10*10^-6;
ef=0.606;
es=1.1;
af=0.012;
as=0.065;
w=10;
qf=;
qs=;
k=0;
for a=-20*10^-6:1*10^-6:20*10^-6
    k=k+1;
    e(k)= a;
    f=@(n)1./(ef*sqrt(n.^2+2*1i*w/af)+es*sqrt(n.^2+2*1i*w/as)).*sin(n*b).*cos(n*a)./(n*b);
    y= quad(f,0,inf);
    d(k)= abs(y);
end
plot(e,d)

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crackpotop

Òø³æ (СÓÐÃûÆø)

¿´ÍƼöµÄÌû×Ó£¬»ý·ÖÓà quadgk£¬³ö½á¹ûÁË~~

¡¾http://blog.sina.com.cn/s/blog_8138d87601013wrk.html¡¿
ËÄ¡¢[q,errbnd] = quadgk(fun,a,b,param1,val1,param2,val2,...)
×ÔÊÊÓ¦Gauss-KronrodÊýÖµ»ý·Ö£¬ÊÊÓÃÓڸ߾«¶ÈºÍÕðµ´ÊýÖµ»ý·Ö£¬Ö§³ÖÎÞÇîÇø¼ä£¬²¢ÇÒÄܹ»´¦Àí¶Ëµã°üº¬ÆæµãµÄÇé¿ö£¬Í¬Ê±»¹Ö§³ÖÑØ×Ų»Á¬Ðøº¯Êý»ý·Ö£¬¸´ÊýÓòÏßÐÔ·¾¶µÄΧµÀ»ý·Ö·¨¡£
×¢ÒâÊÂÏ
1.»ý·ÖÏÞ[a,b]¿ÉÒÔÊÇ[-inf,inf]£¬µ«±ØÐë¿ìËÙË¥¼õ£»
2.±»»ýº¯ÊýÔڶ˵ã¿ÉÒÔÓÐÆæµã£¬Èç¹ûÇø¼äÄÚ²¿ÓÐÆæµã£¬½«ÒÔÆæµãÇø¼ä»®·Ö³É¶à¸ö£¬Ò²¾ÍÊÇËµÆæµãÖ»ÄܳöÏÖÔڶ˵ãÉÏ£»
3.±»»ýº¯Êý¿ÉÒÔ¾çÁÒÕðµ´£»
4.¿ÉÒÔ¼ÆËã²»Á¬Ðø»ý·Ö£¬´ËʱÐèÒªÓõ½'Waypoints'²ÎÊý£¬'Waypoints'ÖÐµÄµã±ØÐëÑϸñµ¥µ÷£»
5.¿ÉÒÔ¼ÆËãΧµÀ»ý·Ö£¬´ËʱÐèÒªÓõ½'Waypoints'²ÎÊý£¬²¢ÇÒΪ¸´Êý£¬¸÷µãÖ®¼äʹÓÃÖ±ÏßÁ¬½Ó£»
6.param,valΪº¯ÊýµÄÆäËü¿ØÖƲÎÊý£¬±ÈÈçÉÏÃæµÄ'waypoints'¾ÍÊÇ£¬¾ßÌå¿´°ïÖú¡£
³öÏÖ´íÎó£º
1.'Reached the limit on the maximum number of intervals in use'
2.'Infinite or Not-a-Number function value encountered'
Àý4 ¼ÆËãÓÐÆæµã»ý·Öint(exp(x)*log(x),0,1)¡£
>>F=@(x)exp(x).*log(x);%Ææµã±ØÐëÔڶ˵ãÉÏ£¬·ñÔòÇëÏȽøÐÐÇø¼ä»®·Ö¡£
>>Q = quadgk(F,0,1)
Q =
   -1.3179
Àý5 ¼ÆËã°ëÎÞÏÞÕðµ´»ý·Öint(x^5*exp(-x)*sin(x),0,inf)¡£

>>F=@(x)x.^5.*exp(-x).*sin(x);
>>fplot(F,[0,100])%»æÍ¼£¬¿´¿´º¯ÊýµÄͼÐÎ
>>[q,errbnd] = quadgk(F,0,inf,'RelTol',1e-8,'AbsTol',1e-12)%»ý·ÖÏÞÖпÉÒÔÓÐinf£¬µ«±ØÐë¿ìËÙÊÕÁ²
q =
-15.0000

errbnd =
9.4386e-009

Àý6 ¼ÆËã²»Á¬Ðø»ý·Ö£¬»ý·Öº¯ÊýΪf(x)=x^5*exp(-x)*sin(x)£¬µ«ÊÇÈËΪ¶¨Òåf(2)=1000£¬f(5)=-100£¬»ý·ÖÇø¼äΪ[1 10]¡£
>>F=@(x)x.^5.*exp(-x).*sin(x);
>>[q,errbnd] = quadgk(F,1,10,'Waypoints',[2 5])%ÏÔÈ»2£¬5Ϊ¼ä¶Ïµã
q =
-10.9408

errbnd =
3.2296e-014
Àý7 ¼ÆËãΧµÀ»ý·Ö£¬ÔÚ¸´ÊýÓòÄÚ£¬»ý·Öº¯Êý1/(2*z-1)£¬»ý·Ö·¾¶ÎªÓÉ[-1-i 1-i 1+i -1+i -1-i]Χ³ÉµÄ¾ØÐα߿ò¡£
>>Waypoints=[-1-i 1-i 1+i -1+i -1-i];
>>plot(Waypoints);%»æÖÆ»ý·Ö·¾¶
>>xlabel('Real axis');ylabel('Image axis');axis([-1.5 1.5 -1.5 1.5]);grid on;
>>Q = quadgk(@(z)1./(2*z - 1),-1-i,-1-i,'Waypoints',[1-i,1+i,-1+i])%×¢Òâ¸÷µã¼äʹÓÃÖ±ÏßÁ¬½Ó
ans =
   0.0000 + 3.1416i
>> quadgk(@(z)1./(2*z - 1),-1-i,-1-i,'Waypoints',Waypoints)%ʹÓÃÕâ¸öµÄЧ¹ûÒ²ÊÇÒ»ÑùµÄ£¬¾ÍÊÇ˵ʼĩµã¿ÉÒÔËæ±ã°ü²»°üº¬ÔÚWaypointsÖС£
ans =
   0.0000 + 3.1416i
2Â¥2015-06-12 18:50:30
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