计算材料学考试

1、分别用前向2点后向2点，对称3点对称5点方法计算f(x=lnx在x=2处的一阶导数和误差，给出不同 h 值(0.5, 0.2, 0.1, 0.05, 0.02, 0.01, 0.005, 0.002,0.001,0.0005, 0.0002, 0.000 仆各方法的误差1.1对称三点法program lximplicit nonedoubleprecisio n,parameter : x=2.0d0 doubleprecisi on : exact,h,f_sym3,diff_sym3h=0.5d0exact=x*(-1do while (h>0write(*,* "En t

2、er value of h (<=0 to stop"read(*,* hif (h<=0.0 thenstop "h<=0"en diff_sym3=(dlog(X+h-dlog(x-h/(2*hdiff_sym3=exact-f_sym3write(*,*"h=",h,"F_SYM3=",f_sym3,"E_SYM3=",diff_sym3 enddoend program lx1.2前向两点法program lximplicit nonedoubleprecisio n,param

3、eter : x=2.0d0 doubleprecisi on : exact,h,f_sym3,diff_sym3 h=0.5d0exact=x*(-1do while (h>0write(*,* "Enter value of h (<=0 to stop"read(*,* hif (h<=0.0 thenstop "h<=0"en diff_sym3=(dlog(x+h-dlog(x/(hdiff_sym3=exact-f_sym3write(*,*"h=",h,"F_SYM3=",f

4、_sym3,"E_SYM3=",diff_sym3 en ddoend program lx1.3后向两点法program lximplicit nonedoubleprecisio n,parameter : x=2.0d0 doubleprecisi on : exact,h,f_sym3,diff_sym3 h=0.5d0exact=x*(-1do while (h>0write(*,* "Enter value of h (<=0 to stop"read(*,* hif (h<=0.0 thenstop "h<

5、=0"en diff_sym3=(dlog(x-dlog(x-h/(hdiff_sym3=exact-f_sym3write(*,*"h=",h,"F_SYM3=",f_sym3,"E_SYM3=",diff_sym3 en ddoend program lx1.4对称五点法program lximplicit nonedoubleprecisio n,parameter : x=2.0d0 doubleprecisi on : exact,h,f_sym5,diff_sym5h=0.5d0exact=x*(-1do whi

6、le (h>0write(*,* "Enter value of h (<=0 to stop"read(*,* hif (h<=0.0d0 thenstop "h<=0"en diff_sym5=(dlog(x-2*h-8*dlog(x-h+8*dlog(x+h-dlog(x+2 *h/(12*hdiff_sym5=exact-f_sym5write(*,"(5(A,F8.6,2X""h=",h,"F_SYM5=",f_sym5,"E_SYM5=",

7、diff_sym5 en ddoend program lx分别用梯形法,Simpson法,Simpson3/8法,Bode法计算2 0cos3dx xn给出8个不同N值下各方法的误差3.1梯形法doubleprecisi on function func(ximplicit nonedoubleprecisi on : xfun c=cos(3*xendfunction funcprogram in tegralimplicit nonein teger : i,n=1doubleprecisi on : pi,limit_dow n,limit_up doubleprecisi on :

8、exact,h,i nteg,summ,diff,x doubleprecisi on : funcexact=-1.0/3.0pi=acos(-1.0d0limit_dow n=0.0d0limit_up=pi/2.0do while(n > 0write(*,* "Enter value of N (eve n,>=2 "read(*,* nif(n<2 thenstop " n<2"en difh=(limit_up-limit_dow n/nsumm=fu nc(limit_dow ndo i=1, n-1x=i*hsum

9、m=summ+fu nc(x*2en ddosumm=summ+fu nc(limit_upin teg=h*summ/2diff=exact-i ntegwrite(*,"(A,l6,2X,5(A,F12.9,2X""N=", n, "h=",h," In teg=",i nteg,"ERROR=",diff enddoend program in tegral3.2辛普森法doubleprecisi on function func(ximplicit nonedoubleprecisi o

10、n : xfun c=cos(3*xendfunction funcprogram in tegralimplicit nonein teger : i,fac ,n=1doubleprecisi on : pi,limit_dow n,limit_up doubleprecisi on : exact,h,i nteg,summ,diff,x doubleprecisi on : funcexact=-1.0/3.0pi=acos(-1.0d0limit_dow n=0.0d0limit_up=pi/2do while(n > 0write(*,* "Enter value

11、of N (eve n,>=2 " read(*,* nif(n<2 thenstop " n<2"en difh=(limit_up-limit_dow n/nsumm=fu nc(limit_dow nfac=2do i=1, n-1if(fac=2 the nfac=4elsefac=2en difx=i*hsumm=summ+fu nc(x*facen ddosumm=summ+fu nc(limit_upin teg=h*summ/3diff=exact-i ntegwrite(*,"(A,l6,2X,5(A,F12.9,2X

12、""N=", n, "h=",h,"I nteg=",i nteg,"ERROR=",diff en ddoend program in tegral3.3辛普森3/8法doubleprecisi on function func(ximplicit nonedoubleprecisi on : xfun c=cos(3*xendfunction funcprogram in tegralimplicit nonein teger : i,n=1doubleprecisi on : pi,limit_do

13、w n,limit_updoubleprecisi on : exact,h,i nteg,summ,diff,x,modi real : fac(3doubleprecisi on : funcexact=-1.0/3.0pi=acos(-1.0d0limit_dow n=O.OdOlimit_up=pi/2do while(n > 0write(*,* "Enter value of N (eve n,>=2 "read(*,* nif(n<2 thenstop " n<2"en difh=(limit_up-limit_do

14、w n/n summ=fu nc(limit_dow n do i=1, n-1 modi=mod(i,3 if(modi=0 the n fac(1=2elseif(modi=1 the nfac(2=3elseif(modi=2 the n fac(3=3 en difx=i*hsumm=summ+fu nc(x*fac(modi+1 en ddosumm=summ+fu nc(limit_upin teg=3*h*summ/8diff=exact-i ntegwrite(*,"(A,l6,2X,5(A,F12.9,2X""N=", n, "

15、;h=",h,"l nteg=",i nteg,"ERROR=",diffen ddoend program in tegral3.4 Bode 法doubleprecisi on function func(ximplicit nonedoubleprecisi on : xfun c=cos(3*xendfunction funcprogram in tegralimplicit nonein teger : i,n=1doubleprecisi on : pi,limit_dow n,limit_updoubleprecisi on :

16、exact,h,i nteg,summ,diff,x,modi real : fac(4doubleprecisi on : funcexact=-1.0/3.0pi=acos(-1.0d0limit down=O.OdOlimit_up=pi/2do while(n > 0write(*,* "Enter value of N (eve n,>=2 "read(*,* nif(n<2 thenstop " n<2"en difh=(limit_up-limit_dow n/nsumm=fu nc(limit_dow n*7do

17、i=1, n-1modi=mod(i,4if(modi=0 the nfac(1=14elseif(modi=1 the nfac(2=32elseif(modi=2 the nfac(3=12elseif(modi=3 the nfac(4=32en difx=i*hsumm=summ+fu nc(x*fac(modi+1en ddosumm=summ+fu nc(limit_up*7in teg=2*h*summ/45diff=exact-i ntegwrite(*,"(A,l6,2X,5(A,F12.9,2X""N=", n, "h=&q

18、uot;,h,"I nteg=",i nteg,"ERROR=",diffen ddoend program in tegral分别用搜索法，牛顿法，弦割法求解f(x=x2-5的正根，改变初始猜测值,观察各方法的收敛行为5.1搜索法doubleprecisi on function func(ximplicit nonedoubleprecisi on : xfun c=x*2-5endfunction funcprogram rootimplicit nonein teger : iter=0doubleprecision : x,dx,guess_s

19、t,tolx,fold,exact,funcexact=sqrt(5.0d0guess_st=1.0d0dx=0.5tolx=1.0d-8x=guess_stfold=f unc(xdo while(abs(dx > tolxiter=ite r+1x=x+dxif(fold*fu nc(x>0.0 the ncycleelsex=x-dxdx=dx/2en difwrite(*,"(l4,6f12.8" iter,x,exact-x enddoend program root5.2牛顿法doubleprecisi on function func(ximplicit nonedoubleprecisi on : xfun c=x*2-5endfunction funcdoubleprecisi on function fun c_prime (ximplicit nonedoubleprecisi on : xfun c_prime=2*xendfunction fun c_primeprogram rootimplicit nonein teger : iter=0doubleprecision : x,xO,dx,guess_st,tolx,exact,func,func_pri