第一篇：信息檢索 第一次大作業(yè) (西南交大,高凡圖書館長(zhǎng))

第一次實(shí)習(xí)作業(yè)

二（1）、在我校圖書館主頁(yè)“書目查詢系統(tǒng)”查找一本專業(yè)相關(guān)圖書，寫出該書的索書號(hào)、館藏復(fù)本數(shù)、館藏地。

書名：機(jī)械原理 索書號(hào)：TH111 I5-3 2007 館第三借閱室（306）

館藏副本數(shù)：2

館藏地：峨眉

(2)利用國(guó)家圖書館 http://004km.cn/檢索一本圖書或?qū)W位論文，使用其在線古籍?dāng)?shù)據(jù)庫(kù)等欄目。

（3）清華大學(xué)圖書館 http://004km.cn/，使用其數(shù)據(jù)庫(kù)導(dǎo)航欄目，獲取常用電子資源平臺(tái)/數(shù)據(jù)庫(kù)的使用指南。

四、（1）google：熟悉其高級(jí)搜索、圖書、地圖、翻譯等工具；利用google學(xué)術(shù)搜索檢索關(guān)于“生物蛋白質(zhì)分子芯片的制造”的中英文文獻(xiàn)，要求列出文獻(xiàn)的題名、作者、出處和摘要信息。

中文文獻(xiàn)

題名：使用多腫瘤標(biāo)志物蛋白質(zhì)芯片診斷系統(tǒng)檢測(cè)卵巢腫瘤 作者：齊軍車軼群

出處：中華檢驗(yàn)醫(yī)學(xué)雜志2003年6且第26卷第6朔c ed ne 2003 ol 壘 摘要【摘要】 目的 研究多腫瘤標(biāo)志物蛋白質(zhì)芯片診斷系統(tǒng)用于卵巢腫瘤的診斷價(jià)值。方法

用多腫瘤標(biāo)志物蛋白質(zhì)芯片診斷系統(tǒng)測(cè)定分析53例卵巢腫瘤患者，12例良性卵巢囊腫和98份正常

對(duì)照人群血清的12種常見的腫瘤標(biāo)志物：甲胎蛋白(AFP)，癌胚抗原(CEA)，神經(jīng)元特異性烯醇化酶

(NSE)，糖原125(CAl25)，糖原153(CA153)，糖原242(CA242)，糖原199(CA199)，前列腺特異性抗

原(PSA)，游離前列腺特異性抗原(f-PSA)，鐵蛋白(FER)，p-人絨毛膜促性腺激素(~-HCG)，人生長(zhǎng) 激素(HGH)。結(jié)果53例惡性卵巢腫瘤患者血清有44例血清腫瘤標(biāo)志物為陽(yáng)性(陽(yáng)性率為

83．O％)，12例良性卵巢囊腫中7例血清腫瘤標(biāo)志物為陽(yáng)性(陽(yáng)性率為58．3％)，98份正常對(duì)照血清

中有2例血清出現(xiàn)腫瘤標(biāo)志物(特異性97．9％)。試驗(yàn)還發(fā)現(xiàn)在部分卵巢癌患者血清中出現(xiàn)NSE、HGH、PSA和f-PSA。結(jié)論多腫瘤標(biāo)志物蛋白質(zhì)芯片診斷系統(tǒng)的應(yīng)用，對(duì)卵巢腫瘤患者術(shù)前腫瘤良

惡性的判定有一定的臨床應(yīng)用價(jià)值。

【關(guān)鍵詞】 卵巢腫瘤； 腫瘤標(biāo)志物； 生物芯片診斷

外文文獻(xiàn)

題名：Proteinchip technology 作者：Heng Zhu?,Michael Snyder 出處：-Current opinion in chemical biology, 2003-Elsevier

Volume 7, Issue 1, February 2003, Pages 55–63 摘要：Abstract Microarray technology has become a crucial tool for large-scale and high-throughput biology.It allows fast, easy and parallel detection of thousands of addressable elements in a single experiment.In the past few years, protein microarray technology has shown its great potential in basic research, diagnostics and drug discovery.It has been applied to analyse antibody–antigen, protein–protein, protein–nucleic-acid, protein–lipid and protein–small-molecule interactions, as well as enzyme–substrate interactions.Recent progress in the field of proteinchips includes surface chemistry, capture molecule attachment, protein labeling and detection methods, high-throughput protein/antibody production, and applications to analyse entire proteomes.四、（二）西南交大到四川大學(xué)公交線路

3）查詢本專業(yè)在國(guó)內(nèi)的排名，并瀏覽排名前三位大學(xué)的相應(yīng)學(xué)院網(wǎng)站，找出該專業(yè)碩士生導(dǎo)師的個(gè)人信息。

前三名：上海交大 華中科技大學(xué) 西安交通大學(xué)

上海交大機(jī)械工程學(xué)院

華中科技大學(xué)機(jī)械工程學(xué)院

西安交大機(jī)械工程學(xué)院

第二篇：西南交大數(shù)值分析第二次大作業(yè)(可以運(yùn)行)

數(shù)值分析第二次大作業(yè)（1）用Lagrange插值法 程序：

function f=Lang(x,y,x0)symst;f=0;n=length(x);for(i=1:n)

l=y(i);for(j=1:i-1)

l=l*(t-x(j))/(x(i)-x(j));end;for(j=i+1:n)

l=l*(t-x(j))/(x(i)-x(j));end

f=f+l;simplify(f);

if(i==n)if(nargin==3)

f=subs(f,'t',x0);else

f=collect(f);

f=vpa(f,6);end end end

x=[1,2,3,-4,5];y=[2,48,272,1182,2262];t=[-1];disp('插值結(jié)果')yt=Lang(x,y,t)disp('插值多項(xiàng)式')yt=Lang(x,y)ezplot(yt,[-1,5]);運(yùn)行結(jié)果：

插值結(jié)果： Yt= 12.0000 插值多項(xiàng)式：

yt =4.0*t^43.0*t + 2.0

（2）構(gòu)造arctan x在[1,6]基于等距節(jié)點(diǎn)的10次插值多項(xiàng)式 程序：

function f=New(x,y,x0)symst;if(length(x)==length(y))

n=length(x);c(1:n)=0.0;else disp('xoíy??êy2?μè￡?');return;end f=y(1);y1=0;xx=linspace(x(1),x(n),(x(2)-x(1)));for(i=1:n-1)for(j=1:n-i)y1(j)=y(j+1)-y(j);end

c(i)=y1(1);

l=t;for(k=1:i-1)

l=l*(t-k);end;

f=f+c(i)*l/factorial(i);simplify(f);

y=y1;

if(i==n-1)if(nargin==3)

f=subs(f,'t',(x0-x(1))/(x(2)-x(1)));else

f=collect(f);

f=vpa(f,6);end end end

>>x=[1,1.5,2,2.5,3,3.5,4,4.5,5,5.5,6];y=[atan(1),atan(1.5),atan(2),atan(2.5),atan(3),atan(3.5),atan(4),atan(4.5),atan(5),atan(5.5),atan(6)];disp('插值多項(xiàng)式')yt=New(x,y)ezplot(yt,[1,6]);hold on ezplot('atan(t)',[1,6])grid on

運(yùn)行結(jié)果： 插值多項(xiàng)式

yt = 1.34684*10^(-10)*t^100.00000104758*t^70.00176296*t^4 + 0.0125826*t^3-0.0640379*t^2 + 0.250468*t + 0.785398（1）用MATLAB自帶spline函數(shù)用于進(jìn)行三次樣條插值 程序：

>>x=[-5,-4,-3,-2,-1,0,1,2,3,4,5];y=[0.03846,0.05882,0.10000,0.20000,0.50000,1.00000,0.50000,0.20000,0.10000,0.05882,0.03846];xi=linspace(-5,5)yi=spline(x,y,xi);plot(x,y,'rp',xi,yi);hold on;syms x fx=1/(1+x^2);ezplot(fx);grid on 運(yùn)行結(jié)果：

由圖可知，三次樣條插值多項(xiàng)式圖像與原函數(shù)圖像基本一致。（2）取第一類邊界條件，用三彎矩法編寫MATLAB程序 程序

functionyi=cubic_spline(x,y,ydot,xi)n=length(x);ny=length(y);h=zeros(1,n);lambda=ones(1,n);mu=ones(1,n);M=zeros(n,1);d=zeros(n,1);for k=2:n h(k)=x(k)-x(k-1);end

for k=2:n-1

lambda(k)=h(k+1)/(h(k)+h(k+1));mu(k)=1-lambda(k);d(k)=6/(h(k)+h(k+1))...*((y(k+1)-y(k))/h(k+1)-(y(k)-y(k-1))/h(k));end

d(1)=6/h(2)*((y(2)-y(1))/h(2)-ydot(1));d(n)=6/h(n)*(ydot(2)-(y(n)-y(n-1))/h(n));A=diag(2*ones(1,n));for i=1:n-1 A(i,i+1)=lambda(i);A(i+1,i)=mu(i+1);end M=Ad;for k=2:n if x(k-1)<=xi & xi<=x(k)yi=M(k-1)/6/h(k)*(x(k)-xi)^3...+M(k)/6/h(k)*(xi-x(k-1))^3...+1/h(k)*(y(k)-M(k)*h(k)^2/6)*(xi-x(k-1))...+1/h(k)*(y(k-1)-M(k-1)*h(k)^2/6)*(x(k)-xi);return;end end

>>a =-5;b = 5;n = 10;h =(b-a)/n;x=a:h:b;y=1./(1+x.^2);ydot=[-5/338,5/338];

xx=a:0.01:b;yy=1./(1+xx.^2);m = length(xx);z = zeros(1,m);for i=1:m z(i)=cubic_spline(x,y,ydot,xx(i));end

plot(x,y,'o',xx,yy,'k:',xx,z,'k-');運(yùn)行結(jié)果： 本題直接利用MATLAB自帶的cftool曲線擬合工具箱完成。擬合結(jié)果：

（1）用多項(xiàng)式擬合：

Linear model Poly1:

f(x)= p1*x + p2 Coefficients(with 95% confidence bounds):

p1 =

-0.8685(-0.8815,-0.8556)

p2 =

30.61(30.48, 30.73)

Goodness of fit:

SSE: 0.1733

R-square: 0.9993

Adjusted R-square: 0.9993

RMSE: 0.1112（2）最小二乘法插值：

Linear interpolant:

f(x)= piecewise polynomial computed from p Coefficients:

p = coefficient structure

Goodness of fit:

SSE: 0

R-square: 1

Adjusted R-square: NaN

RMSE: NaN R-square(確定系數(shù))SSR：Sum of squares of the regression，即預(yù)測(cè)數(shù)據(jù)與原始數(shù)據(jù)均值之差的平方和，公式為：

SST：Total sum of squares，即原始數(shù)據(jù)和均值之差的平方和，公式為：

“確定系數(shù)”是定義為SSR和SST的比值，故

其實(shí)“確定系數(shù)”是通過(guò)數(shù)據(jù)的變化來(lái)表征一個(gè)擬合的好壞。由上面的表達(dá)式可以知道“確定系數(shù)”的正常取值范圍為[0 1]，越接近1，表明方程的變量對(duì)y的解釋能力越強(qiáng)，這個(gè)模型對(duì)數(shù)據(jù)擬合的也較好

4.（1）16點(diǎn)復(fù)合梯形公式： 程序：

function I =T_quad(x,y)n=length(x);m=length(y);h=(x(n)-x(1))/(n-1);a=[1 2*ones(1,n-2)1];I=h/2*sum(a.*y);End 運(yùn)行結(jié)果：

(1)x=0:0.0625:1 y=exp(x)I=T_quad(x,y)x =

Columns 1 through 7

0

0.0625

0.1250

0.1875

0.2500

0.3125

0.3750

Columns 8 through 14

0.4375

0.5000

0.5625

0.6250

0.6875

0.7500

0.8125

Columns 15 through 17

0.8750

0.9375

1.0000 y =

Columns 1 through 7

1.0000

1.0645

1.1331

1.2062

1.2840

1.3668

1.4550

Columns 8 through 14

1.5488

1.6487

1.7551

1.8682

1.9887

2.1170

2.2535

Columns 15 through 17

2.3989

2.5536

2.7183 I =

1.7188

(2)x=1:0.0625:2 y=sin(x)/x I=T_quad(x,y)x =

Columns 1 through 7 1.0000

1.0625

1.1250

1.1875

1.2500

1.3125

1.3750

Columns 8 through 14

1.4375

1.5000

1.5625

1.6250

Columns 15 through 17

1.8750

1.9375

2.0000 y = 0.6116 I = 0.6116（2）8點(diǎn)的復(fù)合simpson公式： 程序：

function I=S_quad(x,y)n=length(x);m=length(y)N=(n-1)/2;h=(x(n)-x(1))/N;a=zeros(1,n);for k=1:N a(2*k-1)=a(2*k-1)+1;a(2*k)=a(2*k)+4;a(2*k+1)=a(2*k+1)+1 end I= h/6*sum(a.*y)end 運(yùn)行結(jié)果：

（1）x=0:0.0625:1 y=exp(x)I=S_quad(x,y)I =

1.7183

（2）x=1:0.0625:2 y=sin(x)/x I=S_quad(x,y)I =

1.6875

1.7500 1.8125

0.6116

（3）三點(diǎn)的Gauss-Legendre積分公式

程序：

function I=G_quad(fun,a,b,N)h=(b-a)/N;I=0;for k=1:N

t=[-sqrt(3/5)0 sqrt(3/5)];A=[5/9 8/9 5/9];

F=feval(fun,h/2*t+a+(k-1/2)*h);

I=I+sum(A.*F)end I=h/2*I;end

運(yùn)行結(jié)果：

(1)fun=inline('exp(x)')I=G_quad(fun,0,1,4)I =

2.2722 I =

5.1898 I =

8.9360 I =

13.7463 I =

1.7183(2)fun=inline('sin(x)/x')I=G_quad(fun,1,2,4)I =

1.5954 I =

3.0143 I =

4.2363 I =

5.2479 I =

0.6560

5、給定初值問(wèn)題y’=-1000(y-x^2)+2x，與y（0）=0，請(qǐng)分別用Euler和預(yù)測(cè)-矯正Euler算法按步長(zhǎng)h=0.1，0.01，0.001，0.0001計(jì)算其數(shù)值，分析其中遇到的現(xiàn)象及問(wèn)題

解：首先根據(jù)可計(jì)算出原函數(shù)為：y=Ce(-1000x)+x2，其中C為常量，為簡(jiǎn)便計(jì)算取C=1，計(jì)算初值x0=0，y0=0。（1）Euler算法 程序：

function[x,y]=Euler_f(ydot_fun,x0,y0,h,N)x=zeros(1,N+1);x(1)=x0;y(1)=y0;for n=1:N x(n+1)=x(n)+h;y(n+1)=y(n)+h*feval(ydot_fun,x(n),y(n));end

format short e ydot_fun=inline('-1000*(y-x*x)+2*x','x','y')[x,y]=Euler_f(ydot_fun,0,0,0.1,10)xx=0:0.1:1 yy=exp(-1000*xx)+xx.*xx d=abs(y-yy)plot(xx,d)title('Eular方法誤差趨勢(shì)圖 h=0.1')運(yùn)行結(jié)果： h=0.1 x =

Columns 1 through 6

0 1.0000e-001 2.0000e-001 3.0000e-001 4.0000e-001 5.0000e-001

Columns 7 through 11

6.0000e-001 7.0000e-001 8.0000e-001 9.0000e-001 1.0000e+000 y =

Columns 1 through 6

0

0 1.0200e+000-9.6940e+001 9.6061e+003-9.5099e+005

Columns 7 through 11

9.4148e+007-9.3207e+009 9.2274e+011-9.1352e+013 9.0438e+015 yy =

Columns 1 through 6

1.0000e+000 1.0000e-002 4.0000e-002 9.0000e-002 1.6000e-001 2.5000e-001

Columns 7 through 11

3.6000e-001 4.9000e-001 6.4000e-001 8.1000e-001 1.0000e+000

d =

Columns 1 through 6

1.0000e+000 1.0000e-002 9.8000e-001 9.7030e+001 9.6060e+003 9.5099e+005

Columns 7 through 11

9.4148e+007 9.3207e+009 9.2274e+011 9.1352e+013 9.0438e+015

h=0.01 x =

Columns 1 through 6 0 1.0000e-002 2.0000e-002 3.0000e-002 4.0000e-002 5.0000e-002

Columns 7 through 11

6.0000e-002 7.0000e-002 8.0000e-002 9.0000e-002 1.0000e-001 y =

Columns 1 through 6

0

0 1.2000e-003-6.4000e-003 6.7200e-002-5.8800e-001

Columns 7 through 11

5.3180e+000-4.7825e+001 4.3047e+002-3.8742e+003 3.4868e+004 xx =

Columns 1 through 6 0 1.0000e-002 2.0000e-002 3.0000e-002 4.0000e-002 5.0000e-002

Columns 7 through 11

6.0000e-002 7.0000e-002 8.0000e-002 9.0000e-002 1.0000e-001 yy =

Columns 1 through 6

1.0000e+000 1.4540e-004 4.0000e-004 9.0000e-004 1.6000e-003 2.5000e-003

Columns 7 through 11

3.6000e-003 4.9000e-003 6.4000e-003 8.1000e-003 1.0000e-002

d =

Columns 1 through 6

1.0000e+000 1.4540e-004 8.0000e-004 7.3000e-003 6.5600e-002 5.9050e-001

Columns 7 through 11

5.3144e+000 4.7830e+001 4.3047e+002 3.8742e+003 3.4868e+004

4.9580e+000 4.8315e+001 4.2983e+002 3.8750e+003 3.4867e+004

h=0.001 x =

Columns 1 through 6 0 1.0000e-003 2.0000e-003 3.0000e-003 4.0000e-003 5.0000e-003

Columns 7 through 11

6.0000e-003 7.0000e-003 8.0000e-003 9.0000e-003 1.0000e-002 y = Columns 1 through 6

0

0 3.0000e-006 8.0000e-006 1.5000e-005 2.4000e-005

Columns 7 through 11

3.5000e-005 4.8000e-005 6.3000e-005 8.0000e-005 9.9000e-005 xx =

Columns 1 through 6 0 1.0000e-003 2.0000e-003 3.0000e-003 4.0000e-003 5.0000e-003

Columns 7 through 11

6.0000e-003 7.0000e-003 8.0000e-003 9.0000e-003 1.0000e-002

yy =

Columns 1 through 6

1.0000e+000 3.6788e-001 1.3534e-001 4.9796e-002 1.8332e-002 6.7629e-003

Columns 7 through 11

2.5148e-003 9.6088e-004 3.9946e-004 2.0441e-004 1.4540e-004 d =

Columns 1 through 6

1.0000e+000 3.6788e-001 1.3534e-001 4.9788e-002 1.8317e-002 6.7389e-003

Columns 7 through 11

2.4798e-003 9.1288e-004 3.3646e-004 1.2441e-004 4.6400e-005

h=0.0001 x =

Columns 1 through 6 0 1.0000e-003 2.0000e-003 3.0000e-003 4.0000e-003 5.0000e-003

Columns 7 through 11

6.0000e-003 7.0000e-003 8.0000e-003 9.0000e-003 1.0000e-002 y =

Columns 1 through 6

0

0 3.0000e-006 8.0000e-006 1.5000e-005 2.4000e-005

Columns 7 through 11

3.5000e-005 4.8000e-005 6.3000e-005 8.0000e-005 9.9000e-005 xx =

Columns 1 through 6 0 1.0000e-004 2.0000e-004 3.0000e-004 4.0000e-004 5.0000e-004

Columns 7 through 11

6.0000e-004 7.0000e-004 8.0000e-004 9.0000e-004 1.0000e-003 yy =

Columns 1 through 6

1.0000e+000 9.0484e-001 8.1873e-001 7.4082e-001 6.7032e-001 6.0653e-001

Columns 7 through 11

5.4881e-001 4.9659e-001 4.4933e-001 4.0657e-001 3.6788e-001 d =

Columns 1 through 6

1.0000e+000 9.0484e-001 8.1873e-001 7.4081e-001 6.7031e-001 6.0651e-001

Columns 7 through 11

5.4878e-001 4.9654e-001 4.4927e-001 4.0649e-001 3.6778e-001

（2）預(yù)測(cè)-矯正Euler算法 程序：

function[x,y]=Euler_r(ydot_fun,x0,y0,h,N)x=zeros(1,N+1);y=zeros(1,N+1);x(1)=x0;y(1)=y0;for n=1:N x(n+1)=x(n)+h;ybar=y(n)+ h*feval(ydot_fun,x(n),y(n))y(n+1)=y(n)+h/2*feval(ydot_fun,x(n),y(n))+ feval(ydot_fun,x(n+1),ybar)end

format short e ydot_fun=inline('-1000*(y-x*x)+2*x','x','y')[x,y]=Euler_r(ydot_fun,0,0,0.001,10)xx=0:0.0001:0.001 yy=exp(-1000*xx)+xx.*xx d=abs(y-yy)plot(xx,d)title('Eular矯正方法誤差趨勢(shì)圖 h=0.001')運(yùn)行結(jié)果： h=0.1 x =

Columns 1 through 6 0 1.0000e-001 2.0000e-001 3.0000e-001 4.0000e-001 5.0000e-001

Columns 7 through 11

6.0000e-001 7.0000e-001 8.0000e-001 9.0000e-001 1.0000e+000 y =

Columns 1 through 6 0 1.0200e+001 1.0083e+006 9.9774e+010 9.8728e+015 9.7692e+020

Columns 7 through 11

9.6667e+025 9.5653e+030 9.4650e+035 9.3657e+040 9.2675e+045 xx =

Columns 1 through 6 0 1.0000e-001 2.0000e-001 3.0000e-001 4.0000e-001 5.0000e-001

Columns 7 through 11

6.0000e-001 7.0000e-001 8.0000e-001 9.0000e-001 1.0000e+000 yy =

Columns 1 through 6

1.0000e+000 1.0000e-002 4.0000e-002 9.0000e-002 1.6000e-001 2.5000e-001

Columns 7 through 11

3.6000e-001 4.9000e-001 6.4000e-001 8.1000e-001 1.0000e+000 d =

Columns 1 through 6

1.0000e+000 1.0190e+001 1.0083e+006 9.9774e+010 9.8728e+015 9.7692e+020

Columns 7 through 11

9.6667e+025 9.5653e+030 9.4650e+035 9.3657e+040 9.2675e+045

h=0.01 x =

Columns 1 through 6 0 1.0000e-002 2.0000e-002 3.0000e-002 4.0000e-002 5.0000e-002

Columns 7 through 11

6.0000e-002 7.0000e-002 8.0000e-002 9.0000e-002 1.0000e-001 y =

Columns 1 through 6 0 1.2000e-001 1.0788e+003 9.7045e+006 8.7302e+010 7.8537e+014

Columns 7 through 11

7.0652e+018 6.3558e+022 5.7177e+026 5.1436e+030 4.6272e+034 xx =

Columns 1 through 6 0 1.0000e-002 2.0000e-002 3.0000e-002 4.0000e-002 5.0000e-002

Columns 7 through 11

6.0000e-002 7.0000e-002 8.0000e-002 9.0000e-002 1.0000e-001 yy =

Columns 1 through 6

1.0000e+000 1.4540e-004 4.0000e-004 9.0000e-004 1.6000e-003 2.5000e-003

Columns 7 through 11

3.6000e-003 4.9000e-003 6.4000e-003 8.1000e-003 1.0000e-002 d =

Columns 1 through 6

1.0000e+000 1.1985e-001 1.0788e+003 9.7045e+006 8.7302e+010 7.8537e+014

Columns 7 through 11

7.0652e+018 6.3558e+022 5.7177e+026 5.1436e+030 4.6272e+034

h=0.001 x =

Columns 1 through 6 0 1.0000e-003 2.0000e-003 3.0000e-003 4.0000e-003 5.0000e-003

Columns 7 through 11

6.0000e-003 7.0000e-003 8.0000e-003 9.0000e-003 1.0000e-002

y =

Columns 1 through 6 0 3.0000e-003 6.5015e-003 1.0255e-002 1.4135e-002 1.8079e-002

Columns 7 through 11

2.2057e-002 2.6053e-002 3.0058e-002 3.4069e-002 3.8084e-002 xx =

Columns 1 through 6 0 1.0000e-003 2.0000e-003 3.0000e-003 4.0000e-003 5.0000e-003

Columns 7 through 11

6.0000e-003 7.0000e-003 8.0000e-003 9.0000e-003 1.0000e-002 yy =

Columns 1 through 6

1.0000e+000 3.6788e-001 1.3534e-001 4.9796e-002 1.8332e-002 6.7629e-003

Columns 7 through 11

2.5148e-003 9.6088e-004 3.9946e-004 2.0441e-004 1.4540e-004 d =

Columns 1 through 6

1.0000e+000 3.6488e-001 1.2884e-001 3.9541e-002 4.1968e-003 1.1316e-002

Columns 7 through 11

1.9542e-002 2.5092e-002 2.9658e-002 3.3864e-002 3.7939e-002

h=0.0001 x =

Columns 1 through 6 0 1.0000e-004 2.0000e-004 3.0000e-004 4.0000e-004 5.0000e-004

Columns 7 through 11

6.0000e-004 7.0000e-004 8.0000e-004 9.0000e-004 1.0000e-003 y =

Columns 1 through 6 0 2.1000e-004-1.8838e-001 1.6937e+002-1.5227e+005 1.3690e+008

Columns 7 through 11-1.2308e+011 1.1065e+014-9.9482e+016 8.9439e+019-8.0410e+022 xx =

Columns 1 through 6 0 1.0000e-004 2.0000e-004 3.0000e-004 4.0000e-004 5.0000e-004

Columns 7 through 11

6.0000e-004 7.0000e-004 8.0000e-004 9.0000e-004 1.0000e-003 yy =

Columns 1 through 6

1.0000e+000 9.0484e-001 8.1873e-001 7.4082e-001 6.7032e-001 6.0653e-001

Columns 7 through 11

5.4881e-001 4.9659e-001 4.4933e-001 4.0657e-001 3.6788e-001 d =

Columns 1 through 6

1.0000e+000 9.0463e-001 1.0071e+000 1.6862e+002 1.5227e+005 1.3690e+008

Columns 7 through 11

1.2308e+011 1.1065e+014 9.9482e+016 8.9439e+019 8.0410e+022

現(xiàn)象和結(jié)論

1.對(duì)于兩種方法，計(jì)算步長(zhǎng)對(duì)計(jì)算結(jié)果穩(wěn)定性有較大影響，步長(zhǎng)選取不當(dāng)時(shí)計(jì)算誤差會(huì)很大；

2.在一定范圍內(nèi)，計(jì)算步長(zhǎng)越小，計(jì)算結(jié)果越穩(wěn)定，結(jié)果誤差越?。?/p>

3.但是并不是計(jì)算步長(zhǎng)越小越好，計(jì)算步長(zhǎng)取值越小計(jì)算次數(shù)就會(huì)增大，初始數(shù)據(jù)誤差積累越嚴(yán)重，也會(huì)導(dǎo)致結(jié)果失真。