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[ÇóÖú] matlabÔÚ¼ÆËãÆ«Î¢·Ö·½³Ìʱ³öÏÖ¡°ÕÒ²»µ½Ö¸¶¨Ä£¿é¡±£¬ÇëÎÊÊÇÈí¼þÎÊÌâÂð£¿

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function ex20_1
%************************************
%Çó½âһάÈÈ´«µ¼Æ«Î¢·Ö·½³ÌµÄÒ»¸ö×ۺϺ¯Êý³ÌÐò
%************************************
m=0;
x=linspace(0,1,20); %xmesh
t=linspace(0,2,20); %tspan
%************
%ÒÔ pde Çó½â
%************
sol=pdepe(m,@ex20_1pdefun,@ex20_1ic,@ex20_1bc,x,t);
u=sol(:,:,1); %È¡³ö´ð°¸
%************
%»æÍ¼Êä³ö
%************
figure(1)
surf(x,t,u)
title('pde ÊýÖµ½â')
xlabel('λÖà x')
ylabel('ʱ¼ä t' )
zlabel('ÊýÖµ½â u')
%*************
%Óë½âÎö½â×ö±È½Ï
%*************
figure(2)
surf(x,t,exp(-t)'*sin(pi*x));
title('½âÎö½â')
xlabel('λÖà x')
ylabel('ʱ¼ä t' )
zlabel('ÊýÖµ½â u')
%*****************
%t=tf=2 ʱ¸÷λÖÃÖ®½â
%*****************
figure(3)
M=length(t); %È¡ÖÕµãʱ¼äµÄϱí
xout=linspace(0,1,100); %Êä³öµãλÖÃ
[uout,dudx]=pdeval(m,x,u(M,,xout);
plot(xout,uout); %»æÍ¼
title('ʱ¼äΪ 2 ʱ,¸÷λÖÃϵĽâ')
xlabel('x')
ylabel('u')
%******************
%pde º¯Êý
%******************
function [c,f,s]=ex20_1pdefun(x,t,u,dudx)
c=pi^2;
f=dudx;
s=0;
%******************-252-
%³õʼÌõ¼þº¯Êý
%******************
function u0=ex20_1ic(x)
u0=sin(pi*x);
%******************
%±ß½çÌõ¼þº¯Êý
%******************
function [pl,ql,pr,qr]=ex20_1bc(xl,ul,xr,ur,t)
pl=ul;
ql=0;
pr=pi*exp(-t);
qr=1;
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