forwdif.m

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function U=forwdif(f,c1,c2,a,b,c,n,m)

%Input - f=u(x,0) as a string 'f'
%      - c1=u(0,t) and c2=u(a,t)
%      - a and b right endpoints of [0,a] and [0,b]
%      - c the constant in the heat equation
%      - n and m number of grid points over [0,a] and [0,b]
%Output - U solution matrix; analogous to Table 10.4

%  NUMERICAL METHODS: Matlab Programs
% (c) 2004 by John H. Mathews and Kurtis D. Fink
%  Complementary Software to accompany the textbook:
%  NUMERICAL METHODS: Using Matlab, Fourth Edition
%  ISBN: 0-13-065248-2
%  Prentice-Hall Pub. Inc.
%  One Lake Street
%  Upper Saddle River, NJ 07458

%Initialize parameters and U

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

%Boundary conditions

U(1,1:m)=c1;
U(n,1:m)=c2;

%Generate first row
U(2:n-1,1)=feval(f,h:h:(n-2)*h)';

%Generate remaining rows of U

for j=2:m
   for i=2:n-1
      U(i,j)=s*U(i,j-1)+r*(U(i-1,j-1)+U(i+1,j-1));
   end
end

U=U';