help leastsquares1
 
    function [tp,yp] = leastsquares1(N,Np);
 
  This function implements the least squares method
  for the problem y'' + y = -t subject to homogeneous
  Dirichlet boundary conditions. N denotes the number 
  of basis functions, and Np denotes the number of
  points in the output arrays for xp and up, for plotting
  the solution. The basis functions are (1-t)*t^k.
 

[tp,yp] = leastsquares1(1,1000);

maxer =

    0.0091

plot(tp,yp,'g'); hold on

[tp,yp] = leastsquares1(10,1000);

maxer =

   3.7026e-14

plot(tp,yp,'r'); hold on

[tp,yp] = leastsquares1(2,1000);

maxer =

    0.0017

plot(tp,yp,'b--'); hold on

[tp,yp] = leastsquares1(3,1000);

maxer =

   7.8999e-05

plot(tp,yp,'k--'); hold on

figure

[tp,yp] = leastsquares1(1,1000);

maxer =

    0.0091

[tp,yp] = leastsquares2(1,1000);

maxer =

    0.0104

plot(tp,yp,'r'); hold on

[tp,yp] = leastsquares2(100,1000);

maxer =

   2.4398e-06

plot(tp,yp,'b'); hold on

[tp,yp] = leastsquares2(2,1000);

maxer =

    0.0039

plot(tp,yp,'g--'); hold on

[tp,yp] = leastsquares2(3,1000);

maxer =

    0.0020

plot(tp,yp,'k--'); hold on

[tp,yp] = galerkin1(3,1000);

maxer =

   2.5670e-05

plot(tp,yp);

help fem1
 
    function [tp,yp] = fem1(N,Np);
 
  This function implements the finite element method with piecewise
  linear continuous basis functions for the PDE y'' + y = -t subject
  to homogeneous Dirichlet boundary conditions. N denotes the number 
  of basis functions, and Np denotes the size of the arrays for tp an
  the function values of the approximation yp for plotting.
 

[tp,yp] = fem1(2,1000);

maxer =

    0.0125

plot(tp,yp);

hold on

[tp,yp] = fem1(100,1000);

maxer =

   1.2228e-05

plot(tp,yp,'r');


[tp,yp] = fem2(3,1000);

maxer =

    0.0054

plot(tp,yp); hold on

[tp,yp] = fem2(1000,1000);

maxer =

   4.3639e-06

plot(tp,yp,'r'); hold on

[tp,yp] = fem2(250,1000);

maxer =

   2.6607e-04

plot(tp,yp,'g--'); hold on

figure

[tp,yp] = fem3(25,1000);

maxer =

   2.8830e-04

plot(tp,yp,'k'); hold on

exit