变步长复化辛普森公式计算积分

2.编写用变步长复化辛普森公式计算积分bf (x)dx的程序。a精品资料0用上面编写的程序计算下列积分并分析计算结果（1 ）0x cos xdx（ 2 ）02 x2 cosx2dx（ 3）1xdx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=mt2=(t1+hn)/2;hn=0;h=(b-a)/n; for j=1:nx(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=%2ds2=%-12.9fs2-s1=%-12.9fn,n,s2,abs(s2-s1);ifabs(s2-s1)eps break;elset1=t2;s1=s2;n=2*n;end end s=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= 2s2=-0.016369112s2-s1=0.944423778n= 4s2=-0.450266122s2-s1=0.433897010n= 8s2=-0.669839370s2-s1=0.219573248n=16s2=-0.781318443s2-s1=0.111479074n=32s2=-0.837710689s2-s1=0.056392245n=64s2=-0.866141900s2-s1=0.028431211n=128s2=-0.880440980s2-s1=0.014299080n=256s2=-0.887620063s2-s1=0.007179083n=512s2=-0.891220052s2-s1=0.003599989n=1024s2=-0.893023740s2-s1=0.001803689s =-0.8930（2 ）s=bianfuhuasimpson(inline(2*x2*cos(x2),0,sqrt(pi),10e-6,2000)n= 2s2=1.076354541s2-s1=2.092222287n= 4s2=0.039359358s2-s1=1.036995183n= 8s2=-0.430456535s2-s1=0.469815894n=16s2=-0.662796649s2-s1=0.232340113n=32s2=-0.778823323s2-s1=0.116026674n=64s2=-0.836827971s2-s1=0.058004648n=128s2=-0.865829756s2-s1=0.029001785n=256s2=-0.880330615s2-s1=0.014500859n=512s2=-0.887581042s2-s1=0.007250427n=1024s2=-0.891206256s2-s1=0.003625214s =-0.8912（3 ）s=bianfuhuasimpson(inline(sqrt(x),0,1,10e-6,2000)n= 2s2=0.489859598s2-s1=0.185121744n= 4s2=0.579745947s2-s1=0.089886349n= 8s2=0.623731522s2-s1=0.043985575n=16s2=0.645384849s2-s1=0.021653327n=32s2=0.656091436s2-s1=0.010706587n=64s2=0.661402273s2-s1=0.005310836n=128s2=0.664042680s2-s1=0.002640407n=256s2=0.665357576s2-s1=0.001314896n=512s2=0