Matlab:导数边界值的有限元(Galerkin)法

 tic;
 % this method is transform from Galerkin method
 %also call it as finit method
 %is used for solving two point BVP which is the first and second term.
 %this code was writen by HU.D.dong in February 11th 2017
 %MATLAB 7.0
 clear;
 clc;
 N=50;
 h=1/N;
 X=0:h:1;
 f=inline('(0.5*pi^2)*sin(0.5*pi.*x)');
 %以下是右端向量:
 for i=2:N
         fun1=@(x) pi^2/2.*sin(pi/2.*x).*(1-(x-X(i))/h);
          fun2=@(x) pi^2/2.*sin(pi/2.*x).*((x-X(i-1))/h);
     f_phi(i-1,1)=quad(fun1,X(i),X(i+1))+quad(fun2,X(i-1),X(i));
     end
  funN=@(x) pi^2/2.*sin(pi/2.*x).*(x-X(N))/h;
     f_phi(N)=quad(funN,X(N),X(N+1));
     %以下是刚度矩阵：
  A11=quad(@(x) 2/h+0.25*pi^2*h.*(1-2*x+2*x.^2),0,1);
  A12=quad(@(x) -1/h+0.25*pi^2*h.*(1-x).*x,0,1);
  ANN=quad(@(x) 1/h+0.25*pi^2*h*x.^2,0,1);
  A=diag([A11*ones(1,N-1),ANN],0)+diag(A12*ones(1,N-1),1)+diag(A12*ones(1,N-1),-1);
  Numerical_solution=A\f_phi;
  Numerical_solution=[0;Numerical_solution];
     %Accurate solution on above以下是精确解
     %%
     for i=1:length(X)
    Accurate_solution(i,1)=sin((pi*X(i))/2)/2 - cos((pi*X(i))/2)/2 + exp((pi*X(i))/2)*((exp(-(pi*X(i))/2)*cos((pi*X(i))/2))/2 + (exp(-(pi*X(i))/2)*sin((pi*X(i))/2))/2);
     end
     figure(1);
     grid on;
     subplot(1,2,1);
      plot(X,Numerical_solution,'ro-',X,Accurate_solution,'b^:');
     title('Numerical solutions vs Accurate solutions');
     legend('Numerical_solution','Accurate_solution');
     subplot(1,2,2);
       plot(X,Numerical_solution-Accurate_solution,'b x');
     legend('error_solution');
     title('error');
     toc;

效果图：