数值积分——复合辛普森求积公式

%%复合辛普森求积公式
%%Y是数值（attribute=0）或具体表达式（attribute=1），interval是求积区间，n是精度（如果是数值，则为数值长度-1）
function CSQF = Compound_Simpson_quadrature_formula(Y,interval,n,attribute)
a = interval(1);b = interval(2);
h = (b-a)/n;lambda = 0.5;
for i = 1:n+1
    X(i) = a+h*(i-1);
end
if attribute == 0
    for i = 1:n
        r = rand(1);
        Y_ave(i) = r*lambda*Y(i)+(1-r*lambda)*Y(i+1);
    end
    sum1 = 0;
    sum2 = 0;
    for i = 1:n
        sum1 = sum1+Y_ave(i);
    end
    for i = 2:n
        sum2 = sum2+Y(i);
    end
    CSQF = vpa(h*(Y(1)+Y(n+1)+4*sum1+2*sum2)/6,8);
elseif attribute ==1
    F = subs(Y,X);
    for i = 1:n
        r = rand(1);
        F_ave(i) =  r*lambda*F(i)+(1-r*lambda)*F(i+1);
    end
    sum1 = 0;
    sum2 = 0;
    for i = 1:n
        sum1 = sum1+F_ave(i);
    end
    for i = 2:n
        sum2 = sum2+F(i);
    end
    CSQF = vpa(h*(F(1)+F(n+1)+4*sum1+2*sum2)/6,8);
end
end

syms x;
Y = exp(x)*sin(x)+log(x+1);
interval=[0 pi];
attribute = 1;
n = 1000;
Compound_Simpson_quadrature_formula(Y,interval,n,attribute)

vpa(int(Y,x,interval),8)

ans =
14.815334
ans =
14.81429