least_square_method1.rar_unknown polynomial_多项式拟合

% 近似解待定参数个数取1个 syms a x real u=a*x; w=diff(u,a); du=diff(u,x); dw=diff(w,x); I=int(-dw*du+w*x,0,1)+subs(w,x,1); a=solve(I) %=================================== %=================================== %近似解待定参数个数取2个 clear syms a1 a2 x real; u=a1*x+a2*x^2; w1=diff(u,a1); w2=diff(u,a2); du=diff(u,x); dw1=diff(w1,x); dw2=diff(w2,x); I1=int(-dw1*du+w1*x,0,1)+subs(w1,x,1)*1; I2=int(-dw2*du+w2*x,0,1)+subs(w2,x,1)*1; [a1,a2]=solve(I1,I2) %================================= %================================= %近似解待定参数个数取3个 clear syms a1 a2 a3 x real; u=a1*x+a2*x^2+a3*x^3; w1=diff(u,a1); w2=diff(u,a2); w3=diff(u,a3); du=diff(u,x); dw1=diff(w1,x); dw2=diff(w2,x); dw3=diff(w3,x); I1=int(-dw1*du+w1*x,0,1)+subs(w1,x,1)*1; I2=int(-dw2*du+w2*x,0,1)+subs(w2,x,1)*1; I3=int(-dw3*du+w3*x,0,1)+subs(w3,x,1)*1; [a1,a2,a3]=solve(I1,I2,I3) %============================== %比较 x=0:0.1:1; u0=1.5*x-x.^3/6; u1=4/3*x; u2=19/12*x-0.25*x.^2; u3=1.5*x-x.^3/6; plot(x,u0,x,u1,x,u2,x,u3); legend('精确解','近似解参数1 个','近似解参数2 个','近似解参数3 个'); xlabel('x') ylabel('u') title('Galerkin法-弱形式')