Matlab:Crank Nicolson方法求解线性抛物方程

 tic;
 clear
 clc
 M=[,,,,,,];%x的步数
 K=M; %时间t的步数
 for p=:length(M)
 hx=/M(p);
 ht=/K(p);
 r=ht/hx^; %网格比
 x=:hx:;
 t=:ht:;
 numerical=zeros(M(p)+,K(p)+);
 numerical(:,)=exp(x); %初始值
 numerical(,:)=exp(t); %边值
 numerical(M(p)+,:)=exp(t+); %边值
 a=-r/*ones(M(p)-,);b=(+r)*ones(M(p)-,);c=-r/*ones(M(p)-,);
 fun1=inline('exp(x+t)','x','t');
 for i=:length(x)
     for j=:length(t)
 Accurate(i,j)=fun1(x(i),t(j));
     end
 end
 d=r/*ones(M(p)-,);e=(-r)*ones(M(p)-,);f=r/*ones(M(p)-,);
 B=diag(d,-)+diag(e,)+diag(f,);
 fun2=inline('','x','t');
 for i=:M(p)-
 for k=:K(p)
     f(i,k)=ht*fun2(x(i+),t(k)+ht/);
 end
 end
 for k=:K(p)
 f(,k)=r/*(numerical(,k+)+numerical(,k));
 f(M(p)-,k)=r/*(numerical(M(p)+,k+)+numerical(M(p)+,k));
 end
 for k=:K(p)
     right_vector=f(:,k)+B*numerical(:M(p),k);
     numerical(:M(p),k+)=chase(a,b,c,right_vector);
 end
 error=numerical(:M(p),:K(p))'-Accurate(2:M(p),2:K(p))';
 error_inf(p)=max(max(error));
 figure(p)
 [X,Y]=meshgrid(x,t);
 subplot(,,)
 mesh(X,Y,Accurate');
 xlabel('x'),ylabel('t');zlabel('Accurate');
 title('the image of Accurate result');
 grid on
 subplot(,,)
 mesh(X,Y,numerical');
 xlabel('x'),ylabel('t');zlabel('numerical');
 title('the image of numerical result');
 grid on
 subplot(,,)
 mesh(X,Y,numerical'-Accurate');
 xlabel('x'),ylabel('t');zlabel('error');
 title('the image of error result');
 grid on
 end
 for k=:length(M)
     H=error_inf(p-)/error_inf(p);
 E_inf(k-)=log2(H);
 end
 figure(length(M)+)
 plot(:length(M)-,E_inf,'-r v');
 ylabel('误差阶数');
 title('Crank nicolson 误差阶数');
 grid on
 toc;