数值分析大作业四

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1、《数值分析》大作业四一、算法设计方案：复化梯形积分法,选取步长为1/500=0.002,迭代误差控制在E<1.0e-10①复化梯形积分法：KfMd兀牙”(d)+/(b)+2工/(d+M)],2k=截断误差为：Rt=厂(77)=-口厂(77),其中77e[a,b]o12/12复化Simpson积分法，选取步长为1/50=0.02,迭代误差控制在E<1.0e-10pjm/n-1②Simpson积分法：ff(x)d-[f(a)+f(b)+4^/(^)+2^f(x2i)],3i=/=i截断误差为:X-晋〃5"[讪。③Guas

2、s积分法选用Gauss-Legendre求积公式：兀艺4/(兀)/=!截断误差为:R=/(2d(n)22n(d!42(2n)+[(2町!]22n1ne(i,i)o选择9个节点：-0.9681602395,-0.8360311073,-0.6133714327,-0.3242534234,0,0.3242534234,0.6133714327,0.8360311073,0.9681602395,对应的求积系数依次为：0.0812743884,0.1806481607,0.2606106964,0.3123470770,0.

3、3302393550,0.3123470770,0.2606106964,0.1806481607,0.0812743884o二、程序源代码:#include#include#include#defineE1.0e-10/****定义函数g和k*****/doubleg(doublea)doubleb;b=exp(4*a)+(exp(a+4)-exp(-a-4))/(a+4);returnb;}doubleK(doublea,doubleb){doublec;c=ex

4、p(a*b);returnc;}严*****复化梯形法******/voidTixing(){doubleu[1001],x[1001],h,c[100l],e;inti,j,k;FILE*fp;fp=fopen("f:/resultO.xls”,”w");h=1.0/1500;for(i=0;i<3001;i++){x[i]=i*h-l;u[i]=g(x[i]);}for(k=0;k<100;k++){e=0;for(i=0;i<1001;i++){for(j=1,c[i]=0;j

5、i],x[j])*u

6、j];u[i]=g(x[i])-h*c[i]-h/2*(K(x[i],x[0])*u[0]+K(x[i],x[N-l])*u[N-l]);e+=h*(exp(4*x[i])-u[i])*(exp(4*x[i])-u[i]);}if(e<=E)break;)for(i=0;i<1001;i++)fprintf(fp；,%.121f,%.121f°,x[i],u[i]);=.£□关(=0dx二二X)N¥号(++「二Sv「OH二PO"二qIHmoJ)(+.±二OIvo.!L)」OJ(++*omo£OJ

7、」e三n二占n三x(++mo-voH-)JOJOWOIHU」(、>spn=nsal?)uodo,ndjseQ=o二p」3二。4=0二x二3二n3qnop()uosdlu一sPOA、薫**沃氓坦uosdlu-s沃沃薫**、」(dj)uso£qsTsn•(寸88Z寸El80020918寸9081.0.寸96929O9Z.OOZZOL寸召IBOVO「滾6EeosooAOL寸EZIE.O>969£9o9zozo9-8寸9022.0•寸8怨寸卜2!80.0t「6<•-「6冑091OO96OM0二E09茫.02*寸ILw19.0.寸

8、需寸^2寸口.0一Q寸me寸ESZ窝E.9ZZE寸1匸29.0^【0二£:0923.0^6^0918960丄"6乂Eqnop)()ssrn?Mp一on^******^^Kssneu氓沃熏畫、xdmsooJ二二二二XXUV0.&TC.&=£)七u-cdj(丰三0IV3也)JE瘩aiq(甲X)七二二nAmd寸)dx9(三nA三x沃寸)dxpqu+u」(?w」faTwx三x)y+ow(ox三乂wroq亠二歹">却三$«(三益丄二nFZ」n*(0e」xsx)H=+mp(oguinti,j,k;FILE*fp;fp=fopen("

9、f:/result2.xls”,"w");for(i=0;i<9;i++)u[i]=g(x[i]);for(k=0;k<50;k++){e=0;for(i=0;i<9;i++){for(j=0,c[i]=0d<9;j++)c[i]+=A[j]*K(x[i],x[j])*u

10、j];u[i]=g(x[i])-c[i];e