% exmp8.m - for Table 5

% This computes m(t)
% by discretizing the interval (0,a)

clear all



i=sqrt(-1);



% Set up basic data

%h=number of divisions per unit length 
h=20

%a=length of interval
a=10

%b=diffusion paramter
b=20

% number of points altogether
N = h*a-1
 
 
 
 
 
% set up tridiagonal matrix

  u=ones(N,1);
  v=ones(N-1,1);
  A=-2*(h^2)*b^(-1)*diag(u)+(h^2)*b^(-1)*diag(v,1)+(h^2)*b^(-1)*diag(v,-1);
  B=(-h/2)*diag(v,1)+(h/2)*diag(v,-1);
  A;
  B;
  C=A+B;
  f=sin((pi/(h*a))*(1:N)');
  format long
  m=zeros(10,1);
  
  
  % compute the norms
  
  for t=1:10
     m(t,1)=norm(expm(t*C)*f,inf);
  end;
  
  m