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

x = 0:.1:1;

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

% print the results
% fprintf('\n   Galerkin G1-2 ')
% fprintf('\n   Your name, ES 301, ')
disp(date)

fprintf('\n      x   approx  exact\n')
fprintf('\n Distance  Quad   Exact   Error \n')
for i = 1:length(x)
  fprintf('   %3.1f  %7.4f  %7.4f %8.4f \n', ...
    x(i),p1(i),p2(i),err(i))
end
fprintf('\n')

plot(x,p1,x,p2)
title('Galerkin G1-G2, Sin Shape Function')
xlabel('Beam length')
ylabel('Deflection'), grid
gtext('Approx'); gtext('Exact')


%  Distance  Quad   Exact   Error 
%   0.0   0.0000   0.0000      NaN 
%   0.1  -0.0450  -0.0399 -12.8807 
%   0.2  -0.0800  -0.0758  -5.5021 
%   0.3  -0.1050  -0.1044  -0.6054 
%   0.4  -0.1200  -0.1227   2.1942 
%   0.5  -0.1250  -0.1290   3.1054 
%   0.6  -0.1200  -0.1227   2.1942 
%   0.7  -0.1050  -0.1044  -0.6054 
%   0.8  -0.0800  -0.0758  -5.5021 
%   0.9  -0.0450  -0.0399 -12.8807 
%   1.0   0.0000  -0.0000 100.0000