m5_3.asv

matlab 相关的数值积分 例如高斯积分 龙贝格积分等等 可参考。

%%%%%%%%%  Gauss Quadrature  %%%%%%%%%%%%%%
fprintf('Orders of the quadratures available are :n=2,3,4,5,6,8,10\n');
n=input('input n:');
a=input('Lower limit:');
b=input('Upper limit:');


a_{2}=[0.5773503  -0.5773503];
a_{3}=[-0.774596669  0  0.774596669];
a_{4}=[-0.861136312  -0.339981043  0.339981043 0.861136312];
a_{5}=[-0.9061798416  -0.538469310  0  0.538469310  0.9061798416];

b_{2}=[1 1];
b_{3}=[0.555555556 0.888888889   0.555555556];
b_{4}=[0.347854845  ]

I=ones(1,n);
x=((b-a)*a_{n}+a*I+b*I)/2;
y=f(x);
Result=(b-a)/2*(sum(b_{n}.*y))