现代数值计算方法(matlab版)第5章(4)new

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1、福建师范大学yêO{数计学院1/17JJII1ÊÙêÈ©Úê©JIBackClose1ÊÙêÈ©Úê©福建师范大学数计学院§5.5pd.¦Èúª2/17ppdúªÑ'(J.±eØy²/Ñ[−1,1]þpd:¦){.½n5.2«m[−1,1]þnpd:TV4õª1dn2nPn(x)=[(x−1)]2nn!dxnJJ.IIJ~5.12n=1,dIdnd2n2Back[(x−1)]=[(x−1)]=2x,dxndxClose[−1,1]þ1pd:x0=0((J~5.10).n=2,ddnd2福建师范大学[(x2−1)n]=[(x2−

2、1)2]=12x2−4,数计学院dxndx2√√3/17[−1,1]þ2pd:x0=−1/3,x1=1/3((J~5.11).n=3,ddnd32n233[(x−1)]=[(x−1)]=120x−72x,dxndx3JJ[−1,1]þ3pd:rrII33Jx0=−,x1=0,x2=.55I,2^½Xê{)5§

3、A¦ÈXêA0=A2=BackClose5/9,A1=8/9.u´[−1,1]þn:pdúªZrr153853f(x)dx≈f−+f(0)+f−,(5.30)−195995福建师范大学数计学院Túªäk5gê°Ý.4/176

4、±epd¦Èúªpd:Ú¦ÈXêXeL.§5.5.2Ï^§SâpdÈ©L1,·±?6±epd¦ÈúªMAT-LABÏ^§SXeµJJII•pd¦ÈúªMATLAB§SJI%magsint.mBackfunctiong=magsint(fname,a,b,n,m)Closenpd:¦ÈXêê°Ý1021福建师范大学数计学院2±0.577350135/17300.8888895±0.7745970.5555564±0.8611360.3478557±0.3399810.652145500.5688899±0.9061800.236927±0.53846

5、90.478629JJ6±0.9324700.13172511±0.6612090.360762II±0.2386190.467914JIL1pd¦Èúªpd:ÚéA¦ÈXêBackClose%^å:^½Úpd¦Èúª¦¼êÈ©%ª:g=magsint(fname,a,b,n,m)fname´ȼê,a,b%©OÈ©eþ,n©ê,mzãpd:ê福建师范大学数计学院switchm6/17case1t=0;A=1;case2t=[-1/sqrt(3),1/sqrt(3)];A=[1,1];case3JJt=[-sqrt(0.6),0.0,sqrt(0

6、.6)];A=[5/9,8/9,5/9];IIcase4Jt=[-0.861136,-0.339981,0.339981,0.861136];IA=[0.347855,0.652145,0.652145,0.347855];BackClosecase5t=[-0.906180,-0.538469,0.0,0.538469,0.906180];A=[0.236927,0.478629,0.568889,0.478629,0.236927];福建师范大学数计学院case67/17t=[-0.93247,-0.661209,-0.238619,0.238619,

7、0.661209,0.93247];A=[0.171325,0.360762,0.467914,0.467914,0.360762,0.171325];otherwiseerror(’§Spd:êU1,2,3,4,5,6!’);endx=linspace(a,b,n+1);JJIIg=0;Jfori=1:nIg=g+gsint(fname,x(i),x(i+1),A,t);BackCloseend%f¼êfunctiong=gsint(fname,a,b,A,t)福建师范大学数计学院g=(b-a)/2*sum(A.*feval(fname,(b-a)/

8、2*t+(a+b)/2));8/17~5.13

9、^pd¦ÈúªÏ^§Smagsint.mOÈ©ZZ114sinxI=dxÚI=dx01+x20xCq.JJ)3MATLAB·-I1II>>magsint(inline(’4./(1+x.^2)’),0,1,2,3)Jans=IBack3.14159122238283Close>>magsint(inline(’4./(1+x.^2)’),0,1,4,4)ans=3.14159265529323福建师范大学数计学院>>magsint(inline(’sin(x)./x’),eps,1,2,3)9/17ans

10、=0.94608307134303>>magsint(inline