% Galerkin deflection for a simple beam
% Galerin G1, G2 Sine approximation
clear

x = 0:0.05:1;

p1 = (x .*x- x)/2;  % exact
p2 = -4/pi^3*sin(pi*x); % Sine
err = (1 - p1 ./p2)*100

% print the results
 fprintf('\n   Galerkin G1 G2 ')
 fprintf('\n   Your name, MENG 421, ')
disp(date)

fprintf('\n Distance  Exact    Sine    Error \n')
for i = 1:length(x)
  fprintf('   %4.2f  %7.3f  %7.3f %8.3f \n', ...
    x(i),p1(i),p2(i),err(i))
end
fprintf('\n')

plot(x,p1,x,p2)
sp = '   '
labtim = [sp 'Galerkin G1-G2, Quad, Sine, Your name, MENG 421,' sp char(date)]
title(labtim)
xlabel('Beam length')
ylabel('Deflection'), grid
gtext('Exact'); gtext('Sine')

%    Galerkin G1 G2 
%    Your name, MENG 421, 25-Jan-2004

%  Distance  Exact    Sine    Error 
%    0.00    0.000    0.000      NaN 
%    0.05   -0.024   -0.020  -17.685 
%    0.10   -0.045   -0.040  -12.881 
%    0.15   -0.064   -0.059   -8.849 
%    0.20   -0.080   -0.076   -5.502 
%    0.25   -0.094   -0.091   -2.772 
%    0.30   -0.105   -0.104   -0.605 
%    0.35   -0.114   -0.115    1.040 
%    0.40   -0.120   -0.123    2.194 
%    0.45   -0.124   -0.127    2.879 
%    0.50   -0.125   -0.129    3.105 
%    0.55   -0.124   -0.127    2.879 
%    0.60   -0.120   -0.123    2.194 
%    0.65   -0.114   -0.115    1.040 
%    0.70   -0.105   -0.104   -0.605 
%    0.75   -0.094   -0.091   -2.772 
%    0.80   -0.080   -0.076   -5.502 
%    0.85   -0.064   -0.059   -8.849 
%    0.90   -0.045   -0.040  -12.881 
%    0.95   -0.024   -0.020  -17.685 
%    1.00    0.000   -0.000  100.000