driver_chandra.m

linear equation routines in matlab

% solve Chandrasekhar H-equation
  
  clear all
 
% reset defauls line thicknesses, .. for graphics 
  set(0, 'defaultaxesfontsize',12,'defaultaxeslinewidth',0.7,...
       'defaultlinelinewidth',0.8,'defaultpatchlinewidth',0.7,...
       'defaulttextfontsize',12)



% define problem parameters. Pass as global variables to chandra.m
  global N c
  
  N = 100;
  c = 0.9;



  x0 = ones(N,1);
  tolf = 1.e-10;
  tolx = 1.e-10;
  maxit = 100;

  % Newton's method
  [x, ithist, iflag] = newtnd( 'chandra', x0, tolf, tolx, maxit );
 
  fprintf('\n  Newton''s Method \n ')
  fprintf(' iter      || x ||_2          || F(x) ||_2       || s ||_2 \n ')
  for i = 1:size(ithist,1)
      fprintf('%4d &$ %13.8e $&$ %13.8e $&$ %13.8e $&$ %13.8e $\\\\ \n ', ithist(i,:))
  end


  mmu = zeros(N,1);
  for i = 1:N
    mmu(i) = (i-0.5)/N;
  end
  plot(mmu,x)
  xlabel('\mu')
  ylabel('H')
  title('Solution of the discretized Chandrasekhar H-eqn')


  % Finite Difference Newton Method
  [x, ithist, iflag] = fdnewtnd( 'chandra', x0, tolf, tolx, maxit );
  
  fprintf('\n  Finite Difference Newton Method \n ')
  fprintf(' iter      || x ||_2          || F(x) ||_2       || s ||_2 \n ')
  for i = 1:size(ithist,1)
      fprintf('%4d &$ %13.8e $&$ %13.8e $&$ %13.8e $&$ %13.8e $\\\\ \n ', ithist(i,:))
  end

  % Shamanskii's Method
  m = maxit;
  [x, ithist, iflag] = shamnd( 'chandra', x0, m, tolf, tolx, maxit );
  
  fprintf('\n  Shamanskii''s Method \n ')
  fprintf(' iter      || x ||_2          || F(x) ||_2       || s ||_2 \n ')
  for i = 1:size(ithist,1)
      fprintf('%4d &$ %13.8e $&$ %13.8e $&$ %13.8e $\\\\ \n ', ithist(i,:))
  end
  
  
  
  % Broyden's Method

  B = eye(N);
  [x, ithist, iflag] = broyden( 'chandra', B, x0, tolf, tolx, maxit );
  
  fprintf('\n  Broyden''s Method \n ')
  fprintf(' iter      || x ||_2          || F(x) ||_2       || s ||_2 \n ')
  for i = 1:size(ithist,1)
      fprintf('%4d &$ %13.8e $&$ %13.8e $&$ %13.8e $\\\\ \n ', ithist(i,:))
  end