fun4.m

关于一的微分方程数值解,一维波动方程初边值问题Crank-Nicholson格式,及追赶法

function A=fun4(t,h,T)
%上机实习四隐式格式;
r=t^2/h^2;
D=100;E=5000;F=3000;L=1;
N=T/t+2;
J=L/h+2;
A(2,J)=0;         %另第一,二行为零
a(1:J-2)=-D*r/4;
b(1:J-2)=1+D*r/2;
c(1:J-2)=-D*r/4;
%%%
    C=[-D*r/4 1+D*r/2 -D*r/4];
    B(1,:)=C(1,2:3);
    B(J-2,J-3:J-2)=C(1,1:2);
    for l=1:J-4
        B(l+1,l:l+2)=C;
    end
for i=3:N
    A(3,1)=0;
    A(3,end)=0;          %用矩阵的左除实现
   for k=1:J-2
    A(3,k+1)=0.5*D*r*A(2,k)+(2-D*r)*A(2,k+1)+0.5*D*r*A(2,k+2)+0.25*D*r*A(1,k)+(-1-D*r/2)*A(1,k+1)+0.25*D*r*A(1,k+2)+t^2*(E*(k)*h*(L-(k)*h)+F);
   end
   A(3,2:J-1)=(zuigan(a,b,c,A(3,2:J-1)'))';
   A(1,:)=A(2,:);
   A(2,:)=A(3,:);
end