華工數(shù)值分析課程設(shè)計(jì)

數(shù)值分析課程設(shè)計(jì)第一題：設(shè)計(jì)思路：我打算用選主元法，先算出每一列，然后把買一列加起來(lái)就是結(jié)果了。2.程序清單：functionx=mat(a,b,flag)ifnargin<3,flag=0;endn=length(b);a=[a,b];fori=1:(n-1)[ar,r]=max(abs(a(i:n,i)));r=r+i-1;ifr>it=a(i,:);a(i,:)=a(r,:);a(r,:)=t;enda((i+1):n,(i+1):(n+1))=a((i+1):n,(i+1):(n+1))-a((i+1):n,i)/a(i,i)*a(i,(i+1):(n+1));a((i+1):n,i)=zeros(n-i,1);ifflag==0,a,endendx=zeros(n,1);x(n)=a(n,n+1)/a(n,n);fori=n-1:-1:1x(i)=(a(i,n+1)-a(i,(i+1):n)*x((i+1):n))/a(i,i);end3.流程圖：我的例子是九階對(duì)角矩陣對(duì)角元素為1,2,3,4,5,6,7,8,9,。流程如圖所示通過(guò)對(duì)比知道，所編的程序算的結(jié)果和inv的結(jié)果一致。x=xspan(1):h:xspan(2);y(1)=y0;forn=1:length(x)-1y(n+1)=y(n)+h*feval(fname,x(n),y(n));endx=x';y=y';function[x,y]=eu2(fname,xspan,y0,h)x=xspan(1):h:xspan(2);y(1)=y0;forn=1:length(x)-1k1=feval(fname,x(n),y(n));y(n+1)=y(n)+h*k1;k2=feval(fname,x(n+1),y(n+1));y(n+1)=y(n)+h*(k1+k2)/2;endx=x';y=y';function[x,y]=ku(fname,xspan,y0,h)x=xspan(1):h:xspan(2);y(1)=y0;forn=1:length(x)-1k1=feval(fname,x(n),y(n));k2=feval(fname,x(n)+h/2,y(n)+h/2*k1);k3=feval(fname,x(n)+h/2,y(n)+h/2*k2);k4=feval(fname,x(n+1),y(n)+h*k3);y(n+1)=y(n)+h*(k1+2*k2+2*k3+k4)/6;endx=x';y=y';流程圖：精確值如上圖。歐拉法，h=0.025歐拉法，h=0.1改進(jìn)歐拉，h=0.05改進(jìn)歐拉h(huán)=0.1龍格法，h-0.1.比較表格：X的值11.11.21.31.41.51.61.71.81.92精確值00.34590.86661.60722.62043.96775.72107.963910.793614.323118.6831歐拉h(huán)=0.02500.32550.81651.51642.47573.75395.42017.555110.252914.584717.7914歐拉h(huán)=0.100.27180.68481.27702.09353.18744.62086.46648.809111.748015.3982改進(jìn)歐拉h(huán)=0.0500.34490.86431.60312.61423.95895.70927.948710.774414.299318.6542改進(jìn)歐拉h(huán)=0.100.34240.85831.59272.59833.93645.67897.909210.724514.237418.5789龍格h=0.100.34590.86661.60722.62033.96765.72097.963810.793514.322918.6829由以上表格可知，在相同步長(zhǎng)的情況龍格法比改進(jìn)歐拉法精確，改進(jìn)歐拉法比歐拉法精確；在相同方法情況，步長(zhǎng)越小越精確

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