Matlab-7:偏微分方程数值解法-李荣华-有限元解导数边界值的常微分（Galerkin方法）

p47.（实习题-李荣华）用线性元求下列边值问题的数值解

 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
 %MATLAB 7.0
 clear;
 clc;
 N=;
 h=/N;
 X=:h:;
 f=inline('(0.5*pi^2)*sin(0.5*pi.*x)');
 %以下是右端向量:
 for i=:N
         fun1=@(x) pi^/.*sin(pi/.*x).*(-(x-X(i))/h);
          fun2=@(x) pi^/.*sin(pi/.*x).*((x-X(i-))/h);
     f_phi(i-,)=quad(fun1,X(i),X(i+))+quad(fun2,X(i-),X(i));
     end
  funN=@(x) pi^/.*sin(pi/.*x).*(x-X(N))/h;
     f_phi(N)=quad(funN,X(N),X(N+));
     %以下是刚度矩阵：
  A11=quad(@(x) /h+0.25*pi^*h.*(-*x+*x.^),,);
  A12=quad(@(x) -/h+0.25*pi^*h.*(-x).*x,,);
  ANN=quad(@(x) /h+0.25*pi^*h*x.^,,);
  A=diag([A11*ones(,N-),ANN],)+diag(A12*ones(,N-),)+diag(A12*ones(,N-),-);
  Numerical_solution=A\f_phi;
  Numerical_solution=[;Numerical_solution];
     %Accurate solution on above以下是精确解
     %%
     for i=:length(X)
    Accurate_solution(i,)=sin((pi*X(i))/)/ - cos((pi*X(i))/)/ + exp((pi*X(i))/)*((exp(-(pi*X(i))/)*cos((pi*X(i))/))/ + (exp(-(pi*X(i))/)*sin((pi*X(i))/))/);
     end
     figure();
     grid on;
     subplot(,,);
      plot(X,Numerical_solution,'ro-',X,Accurate_solution,'b^:');
     title('Numerical solutions vs Accurate solutions');
     legend('Numerical_solution','Accurate_solution');
     subplot(,,);
       plot(X,Numerical_solution-Accurate_solution,'b x');
     legend('error_solution');
     title('error');
     toc;