变步长复化辛普森公式计算积分.doc

_2. 编写用变步长复化辛普森公式计算积分 的程序。用上面编写的程序计算下列积分并分析计算结果（1） （2） （3）程序：function S=bianfuhuasimpson(fx,a,b,eps,M)% 变步长复合simpson求积公式% 调用方式： S=fuhuasimpson(fx,a,b,epsilon)% fx - 求积函数（函数文件）% a, b - 求积区间% eps - 计算精度% M-最大允许输出划分数n=1;h=(b-a)/n;T1=h*(feval(fx,a)-feval(fx,b)/2;Hn=h*feval(fx,(a+b)/2);S1=(T1+2*Hn)/3;n=2*n; % 最好与倒数第三行保持一致（变步长）while n=M T2=(T1+Hn)/2; Hn=0; h=(b-a)/n; for j=1:n x(j)=a+(j-1/2)*h; y(j)=feval(fx,x(j); Hn=Hn+y(j); end Hn=h*Hn; S2=(T2+2*Hn)/3; fprintf( n=%2d S2=%-12.9f S2-S1=%-12.9fn,n,S2,abs(S2-S1);if abs(S2-S1)eps break;else T1=T2; S1=S2; n=2*n;endendS=S2;% 达到下列条件之一，则运算终止:% (1).abs(S2-S1)M% 输入1：S=bianfuhuasimpson(inline(sqrt(x)*cos(x),0,pi,10e-6,2000)% 输入2：S=bianfuhuasimpson(inline(2*x2*cos(x2),0,sqrt(pi),10e-6,2000)% 输入3：S=bianfuhuasimpson(inline(sqrt(x),0,1,10e-6,2000)输出结果：（1）S=bianfuhuasimpson(inline(sqrt(x)*cos(x),0,pi,10e-6,2000) n= 2 S2=-0.016369112 S2-S1=0.944423778 n= 4 S2=-0.450266122 S2-S1=0.433897010 n= 8 S2=-0.669839370 S2-S1=0.219573248 n=16 S2=-0.781318443 S2-S1=0.111479074 n=32 S2=-0.837710689 S2-S1=0.056392245 n=64 S2=-0.866141900 S2-S1=0.028431211 n=128 S2=-0.880440980 S2-S1=0.014299080 n=256 S2=-0.887620063 S2-S1=0.007179083 n=512 S2=-0.891220052 S2-S1=0.003599989 n=1024 S2=-0.893023740 S2-S1=0.001803689 S = -0.8930（2）S=bianfuhuasimpson(inline(2*x2*cos(x2),0,sqrt(pi),10e-6,2000) n= 2 S2=1.076354541 S2-S1=2.092222287 n= 4 S2=0.039359358 S2-S1=1.036995183 n= 8 S2=-0.430456535 S2-S1=0.469815894 n=16 S2=-0.662796649 S2-S1=0.232340113 n=32 S2=-0.778823323 S2-S1=0.116026674 n=64 S2=-0.836827971 S2-S1=0.058004648 n=128 S2=-0.865829756 S2-S1=0.029001785 n=256 S2=-0.880330615 S2-S1=0.014500859 n=512 S2=-0.887581042 S2-S1=0.007250427 n=1024 S2=-0.891206256 S2-S1=0.003625214 S = -0.8912（3）S=bianfuhuasimpson(inline(sqrt(x),0,1,10e-6,2000) n= 2 S2=0.489859598 S2-S1=0.185121744 n= 4 S2=0.579745947 S2-S1=0.089886349 n= 8 S2=0.623731522 S2-S1=0.043985575 n=16 S2=0.645384849 S2-S1=0.021653327 n=32 S2=0.656091436 S2-S1=0.010706587 n=64 S2=0.661402273 S2-S1=0.005310836 n=128 S2=0.664042680 S2-S1=0.002640407 n=256 S2=0.665357576 S2-S1=0.001314896 n=512 S2=0.666013