(F,x0,x(k+1));РendРq=q*(b-a)/n/6;Р用辛普森公式计算多重积分有:Р>> syms x y;F=exp(-x.*y);Р>> binesimpson2(F,'x',0,1,4),y,0,1,4)Рs =Р 0.7966Р对于多重积分的Gauss公式,先编制Gauss公式的M文件,其中要用到函数GAUSSPOINTS,使用格式及作用如下:РGAUSSPOINTS points for Gaussian quadrature Р Р [nodes, weights] = gausspoints(nquad)Р computes the nodes and weights for Gaussian quadrature with nquad (<=5) quadrature points on Р the standard interval [-1,1]Р编制的M文件为:Рfunction q=gaussquad(F,x0,a,b,n)Р%Gauss求积公式Р%F—被积函数Р%x0—被积函数自变量Р%[a,b]积分区间Р%n—节点个数Рsyms t;РF=subs(F,x0,(b-a)/2*t+(a+b)/2);Р[x,A]=gausspoints(n);Рq=(b-a)/2*sum(A.*subs(F,t,x));Р用Gauss求积公式计算多重积分有:Р>> clearР>> syms x y;F=exp(-x.*y);Р>> s=gaussquad(gaussquad(F,x,0,1,4),y,0,1,4)Рs =Р0.7966Р(2)若区域,用复合辛普森公式(取n=4)求此积分.Р>> syms x y;F=exp(-x.*y);Р>> binesimpson2(F,y,0,sqrt(1-x^2),4),x,0,1,4)Рs =Р 0.6701
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