finedif.m

国外计算机科学教材系列 numerial method using matlab (third edition)

function U = finedif(f,g,a,b,c,n,m)
% U = finedif('f','g',0,1,4,10,10)
%Input - f=u(x,0) as a string 'f'
%      - g=ut(x,0) as a string 'g'
%      - a and b right endpoints of [0,a] and [0,b]
%      - c the constant in the wave equation
%      - n and m number of grid points over [0,a] and [0,b]
%Output - U solution matrix; analogous to Table 10.1

%Initialize parameters and U

h = a/(n-1);
k = b/(m-1);
r = c*k/h;
r2=r^2;
r22=r^2/2;
s1 = 1 - r^2;
s2 = 2 - 2*r^2;
U = zeros(n,m);

%Comput first and second rows

for i=2:n-1
   U(i,1)=feval(f,h*(i-1));
   U(i,2)=s1*feval(f,h*(i-1))+k*feval(g,h*(i-1)) ...
          +r22*(feval(f,h*i)+feval(f,h*(i-2)));
end
    
%Compute remaining rows of U

for j=3:m,
  for i=2:(n-1),
     U(i,j) = s2*U(i,j-1)+r2*(U(i-1,j-1)+U(i+1,j-1))-U(i,j-2);
  end
end

U=U';

function e1=f(t)
e1=sin(pi.*t)+sin(2.*pi.*t);

function e2=g(t)
e2=0;