数值分析-第九章计算实习题答案-昆工.docx

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1、程序:cic;clear;a二l;b=2;%定义域h = 0.05;% 步长n=(b-a)/h;y0=l;%初值f= (x,y) 1/x 八 2-y/x;% 微分函数Xn=linspace(a,b,n+1);%将定义域分为n等份Yn 二 zeros(Ln);% 结果矩阵Yn=y0;%赋初值%以下根据改进欧拉公式求解for i=l:nxn=Xn(i);xnn=Xn(i + l);yn=Yn(i);yp=yn+h*f(xn,yn);yc=yn + h*f(xnn,yp);yn=(yp+yc)/2;Yn(i + l)=yn;endXn=Yn;%以下根据经典四阶R-K法公式求解for i=l:nxn

2、= Xn(i);yn=Yn(i);kl=f(xn,yn);k2=f(xn+h/2,yn + h/2*kl);k3=f(xn+h/2,yn + h/2*k2);k4=f(xn+h,yn+h*k3);yn = yn+h/6*(kl+2*k2+2*k3+k4);Yn(i+l)=yn;enddispC改进欧拉法 四阶经典R-K法)disp(Xn Yn)结果如下：改进欧拉法10.998870.995770.991140.985320.97857四阶经典R-K法10.998850.99780.996940.996340.996030.971110.996060.963110.996450.95470.99

3、7230.945980.998410.9370510.927981.0020.918831.00440.909641.00730.900451.01060.891291.01430.882181.01840.873151.02290.864211.02780.855381.03310.846651.0388(b)程序：cic;clear;a=0;b=l;%定义域H = 0.1 0.025 0.01;%步长yO = 1/3;% 初值f= (x,y) -50*y+50*x/x2+2*x;%微分函数 xi=linspace(a,b,ll);Y = l/3*exp(-50*xi)+xiC2;% 准确解

4、 Ym=zeros(l,ll);for j=l:3h = H(j)；n=(b-a)/h;Xn = linspace(a,b,n + 1)；%将定义域分为n等份Yn 二 zeros(l,n);% 结果矩阵Yn=yO;%赋初值for i=l:nxn=Xn(i);yn=Yn(i);kl=f(xn,yn);k2=f(xn+h/2 ,yn+h/2*kl);k3 = f(xn+h/2,yn + h/2*k2);k4 = f(xn+h,yn+h*k3);yn=yn + h/6*(kl+2*k2+2*k3+k4);Yn(i + l)=yn;endfor k= 1:11m=0.1/h;Ym(k)=Yn(l+(k

5、-l)*m);enddelta=Ym-Y;fprintf(,步长为：%d n, h);误差）；disp(1四阶经典R-K法 准确解disp(Ym Y delta)end结果如下：步长为：1.000000e-01四阶经典R-K法0.333334.605563.062864.05118441.6235e+052.2256e+063.0509e+074.1823e+085.7333e+097.8594e+10四阶经典R-K法0.333334.605563.062864.05118441.6235e+052.2256e+063.0509e+074.1823e+085.7333e+097.8594e+1

6、0准确解0.333330.0122460.0400150.090.160.250.360.490.640.811、口I天差04.593263.022863.96118431.6235e+052.2256e+063.0509e+074.1823e+085.7333e+097.8594e+10、0I天差四阶经典R-K法步长为：2.500000e-02准确解0.333330.3333300.0130150.0122460.000768940.0400630.0400154.82e-050.0900370.093.6857e-050.160040.163.6723e-050.250040.253.67

7、22e-050.360040.363.6722e-050.490040.493.6722e-050.640040.643.6722e-050.81004113.6722e-05步长为：1.000000e-02四阶经典R-K法准确解误差0.333330.3333300.0122560.0122469.5673e-060.0400160.0400157.8252e-070.0900010.096.6347e-070.160.166.6226e-070.250.256.6225e-070.360.366.6225e-070.490.496.6225e-070.640.646.6225e-070.810.816.6225e-07116.6225e-070.813.6722e-05由结果可知，步长越小，结果越精确。