2018数模国赛a题

function heat_conduction()
options={'L','N' ,'M','alfa','lambda(0.5)',}; 
topic='seting'; 
lines=1; 
def={'5','100','1000','5.57467976468964e-10','0.5'}; 
h=inputdlg(options,topic,lines,def); 
L=eval(h{1}); 
N=eval(h{2}); 
M=eval(h{3}); 
alfa=eval(h{4}); 
lambda=eval(h{5});.5 
%*************************************************** 
h=L/N;%???? 
z=0:h:L; 
z=z'; 
tao=lambda*h^2/alfa;%???? 
tm=M*tao;%tm 
t=0:tao:tm; 
t=t';  
T=zeros(N+1,M+1); 
Ti=init_fun(z); 
To=border_funo(t); 
Te=border_fune(t); 
T
T(1,:)=To; 
T(N+1,:)=Te;  
for k=1:M 
m=2; 
while m<=N 
T(m,k+1)=lambda*(T(m+1,k)+T(m-1,k))+(-2*lambda+1)*T(m,k); 
m=m+1; 
end; 
end;  
for i=1:M+1 
X(:,i)=z; 
end; 
for j=1:N+1 
Y(j,:)=t; 
end 
mesh(X,Y,T); 
view([1 -1 1]); 
xlabel('Z'); 
ylabel('t'); 
zlabel('T'); 

function y=init_fun(z)% 
y=48.08;
return 

function y=border_funo(t)%z=0 
y=48.08; 
return 

function y=border_fune(t)%z=L 
y=48.083; 
return