复合梯形公式

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