资源描述：
《函数逼近和微分方程求解》由会员上传分享，免费在线阅读，更多相关内容在应用文档-天天文库。
1、实验四函数逼近和微分方程求解一、实验内容：1.某种合金在一种添加剂的不同浓度下进行实验，得到如下数据：浓度x10.015.020.025.030.0抗压强度y25.229.831.231.729.4（1）已知y与x的关系适合如下模型：，试用最小二乘法编程计算a,b,c；（2）求出平方误差，并作出拟合曲线。M文件：function[]=zxecnh2(X,Y)n=length(X);k00=0;fori=1:nk00=k00+1;endk01=0;fori=1:nk01=k01+X(i);endk02=0;for
2、i=1:nk02=k02+X(i)*X(i);endk11=0;fori=1:nk11=k11+X(i)*X(i);endk12=0;fori=1:nk12=k12+X(i)*X(i)*X(i);endk22=0;fori=1:nk22=k22+X(i)*X(i)*X(i)*X(i);endk0y=0;fori=1:nk0y=k0y+Y(i);endk1y=0;fori=1:nk1y=k1y+X(i)*Y(i);endk2y=0;fori=1:nk2y=k2y+X(i)*X(i)*Y(i);endA=[k00k
3、01k02;k01k11k12;k02k12k22];B=[k0y;k1y;k2y];C=AB;p=C(1);q=C(2);r=C(3);symsx;'拟合的二次函数为：'f=p+q*x+r*x*xl=0;fori=1:nl=l+((p+q*X(i)+r*X(i)*X(i))-Y(i))*((p+q*X(i)+r*X(i)*X(i))-Y(i));end'该拟合函数的平方误差为：'L运行程序：>>X=[10.015.020.025.030.0];>>Y=[25.229.831.231.729.4];>>zxe
4、cnh2(X,Y)ans=拟合的二次函数为：f=(1061723612152537*x)/562949953421312-(1513209474796397*x^2)/36028797018963968+2994893752201639/281474976710656ans=该拟合函数的平方误差为：l=0.2680>>X=[10.015.020.025.030.0];>>Y=[25.229.831.231.729.4];>>plot(X,Y,'r*');2.解初值问题：（1）分别用Euler法和、改进的Eule
5、r法和四阶R-K方法编程计算（取步长）；（2）将所得数值解以表格形式列出，并与真解作比较。（可打印）改进的Euler法：function[x,y]=gjEuler(dfun,span,y0,h)x=span(1):h:span(2);y(1)=y0;forn=1:length(x)-1k1=feval(dfun,x(n),y(n));y(n+1)=y(n)+h*k1;k2=feval(dfun,x(n+1),y(n+1));y(n+1)=y(n)+h*(k1+k2)/2endx=x';y=y';dfun=inl
6、ine('x*y^2');>>[x,y]=gjEuler(dfun,[0,1],1,0.1)y=1.0000000000000001.005000000000000y=1.0000000000000001.0050000000000001.020354410175500y=1.0000000000000001.0050000000000001.0203544101755001.047026380600415y=Columns1through41.0000000000000001.0050000000000001
7、.0203544101755001.047026380600415Column51.086794642471522y=Columns1through41.0000000000000001.0050000000000001.0203544101755001.047026380600415Columns5through61.0867946424715221.142568236682096y=Columns1through41.0000000000000001.0050000000000001.02035441017
8、55001.047026380600415Columns5through71.0867946424715221.1425682366820961.218971212542743y=Columns1through41.0000000000000001.0050000000000001.0203544101755001.047026380600415Columns5through81.08
