数值分析 06-07试卷

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1、2006(A)HÆ(+%)H0S000112F^
Y150%,F1$#'nz0y4e0123456789%("!-841;8:9/96573.<2084.)1.(11%)<83%Z1nx+1In=dx,n=0,1,2,···04x+1g#{C'g#akx
$1*&8*2.(11%)#S$f(x)=2x−lnx−7=0d
Z,BVÆ4j
va
3.(11%)GausstU#?rx$120x14

2、202x2=−7−131x36$2*&8*4.(11%)+rx$ab0x1b1cabx2=b2,(1)0cax3b3a,b,c,b1,b2,b3iaRabc6=0.^+?$(1)Gauss-Seidel)_

3、f;
$3*&8*5.(112%)Xf(x)∈C[a,b].S}*3!sH(x)[′′′′′′′′H(a)=f(a),H(b)=f(b),H(b)=f(b),H(b)=f(

4、b).$4*&8*16.(11%)Xf(x)=,x∈[−1,1].Sf(x)[−1,1]W1:}!s3+xp1(x)=c0+c1x.$5*&8*Zb3f(x)dx,7.(12%)Xf∈C[a,b],I(f)=+S3%I(f)S3-ab−aa+2bQ(f)=f(a)+3f.(2)43(a)S3-(2)aB
42b−a′′′(b)I(f)−Q(f)=f(η),η∈(a,b).272b−a(c)Tan,9h=,xi=a+ih(i=0,1,···,n).^.

5、S3-(2)&2nI(f)−Qn(f)S3-Qn(f),S5qhlim→0h3.$6*&8*8.(11%)+h%$le(y′(x)=f(x,y(x)),a≤x≤b,y(a)=η.b−aTan,9h=n,xi=a+ih,i=0,1,2,···,n.(a)Saα,[oS?-E
AG(=aSD>m6=a
1hyi+1=(yi+yi−1)+[αf(xi+1,yi+1)−f(xi,yi)+(α−1)f(xi−1,yi−1)].(3)24(b)}*"=p-W

6、-(3).}*–u-d.–u-℄7-
$7*&8*9.(11%)+le∂u∂2u(x,t)=(x,t),0

7、.1)b
$8*&8*