chap3_9.m

利用MATLAB解决偏微分方程中的一些问题,如插值求解

 function[Y1,Y2,E1]=chap3_9(h,tao,A)   %习题3.9
a=2;r=a*tao/h^2;
for k=1:1/tao+1
  for i=1:1/h+1
      U(k,i)=0;
  end
end
for i=1:1/h+1
    X(1,i)=(i-1)*h;U(1,i)=exp(X(1,i))*sin(0.5);
end

for k=1:1/tao+1
    T(1,k)=(k-1)*tao;U(k,1)=sin(0.5-T(1,k));U(k,1/h+1)=exp(1)*sin(0.5-T(1,k));
end
for k=2:1/tao+1
    for i=2:1/h
    U(k,i)=(1-2*r)*U(k-1,i)+r*(U(k-1,i-1)+U(k-1,i+1))+tao*(-exp(X(1,i))*(cos(0.5-T(1,k-1))+2*sin(0.5-T(1,k-1))));
end
end
for j=1:length(A)
Y1(1,j)=U(ceil(A(1,j)/tao+1),ceil(0.5/h+1));%ceil()为加入正小数至最近整数．
Y2(1,j)=exp(0.5)*sin(0.5-A(1,j));E1(1,j)=abs(Y1(1,j)-Y2(1,j));
end