复合梯形公式
复合梯形公式:
h=1/8;n=8;
format long
X=zeros(1,n);Y=zeros(1,n); X(1)=0;Y(1)=1;
i=2;
for k=1:n
X(i)=h*k;Y(i)=sin(X(i))/X(i);
i=i+1;
end
B=sum(Y)-Y(n+1)-Y(1); C=Y(1)+2*B+Y(n+1);
T=h*(1/2)*C
结果:
T =
0.94569086358270 复合辛普森公式:
h=1/4;n=4;
format long
X=zeros(1,n);Y=zeros(1,n);D=zeros(1,n);E=zeros(1,n);
X(1)=0;Y(1)=1;E(1)=1/8; i=2;
for k=1:n
X(i)=h*k;Y(i)=sin(X(i))/X(i);
i=i+1;
end
B=sum(Y)-Y(n+1)-Y(1); C=Y(1)+2*B+Y(n+1);
j=1;
for k=0:n-1
D(j)=(2*k+1)*(1/8);E(j)=sin(D(j))/D(j);
j=j+1;
end
S=h*(1/6)*(4*sum(E)+C) 结果:
S =
0.94608331088847 科特斯公式:
h=1/4;n=4;
format long
X=zeros(1,n);Y=zeros(1,n);D=zeros(1,n);E=zeros(1,n);
X(1)=0;Y(1)=1;E(1)=1/8; i=2;
for k=1:n
X(i)=h*k;Y(i)=sin(X(i))/X(i);
i=i+1;
end
C=(1/90)*(7*Y(1)+32*Y(2)+12*Y(3)+32*Y(4)+7*Y(5))
结果:
C =
0.94608300406367