% expm7.m - for Table 4
% This computes \norm T_t\norm_\infty
% by discretizing the interval (0,a)


clear all

% 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);
  %B(1,1)=h/2;
  %B(N,N)=-h/2;
  A;
  B;
  C=A+B;
  
  % compute the semigroup norms
  
  format long
  tnorm=zeros(N,1);
  for t=1:10
        Tnorm(t,1)=norm(expm((t)*C),inf);
  end;
     
  
  Tnorm