计算材料学考试Word文件下载.docx
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计算材料学考试Word文件下载.docx
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if(h<
=0.0then
stop"
h<
=0"
endif
f_sym3=(dlog(X+h-dlog(x-h/(2*h
diff_sym3=exact-f_sym3
write(*,*
"
h="
h,"
F_SYM3="
f_sym3,"
E_SYM3="
diff_sym3enddo
endprogramlx
1.2前向两点法
f_sym3=(dlog(x+h-dlog(x/(h
1.3后向两点法
f_sym3=(dlog(x-dlog(x-h/(h
1.4对称五点法
exact,h,f_sym5,diff_sym5
=0.0d0then
f_sym5=(dlog(x-2*h-8*dlog(x-h+8*dlog(x+h-dlog(x+2*h/(12*h
diff_sym5=exact-f_sym5
write(*,"
(5(A,F8.6,2X"
F_SYM5="
f_sym5,"
E_SYM5="
diff_sym5enddo
分别用梯形法,Simpson法,Simpson3/8法,Bode法计算
20cos3d
xx
π
⎰
给出8个不同N值下各方法的误差
3.1梯形法
doubleprecisionfunctionfunc(x
doubleprecision:
x
func=cos(3*x
endfunctionfunc
programintegral
integer:
i,n=1
pi,limit_down,limit_up
exact,h,integ,summ,diff,x
func
exact=-1.0/3.0
pi=acos(-1.0d0
limit_down=0.0d0
limit_up=pi/2.0
dowhile(n>
0
EntervalueofN(even,>
=2"
read(*,*n
if(n<
2then
n<
2"
h=(limit_up-limit_down/n
summ=func(limit_down
doi=1,n-1
x=i*h
summ=summ+func(x*2
enddo
summ=summ+func(limit_up
integ=h*summ/2
diff=exact-integ
(A,I6,2X,5(A,F12.9,2X"
N="
n,"
Integ="
integ,"
ERROR="
diffenddo
endprogramintegral
3.2辛普森法
i,fac,n=1
limit_up=pi/2
fac=2
if(fac==2then
fac=4
else
summ=summ+func(x*fac
integ=h*summ/3
diff
3.3辛普森3/8法
exact,h,integ,summ,diff,x,modireal:
fac(3
modi=mod(i,3
if(modi==0then
fac(1=2
elseif(modi==1then
fac(2=3
elseif(modi==2then
fac(3=3
summ=summ+func(x*fac(modi+1
integ=3*h*summ/8
3.4Bode法
fac(4
summ=func(limit_down*7
modi=mod(i,4
fac(1=14
fac(2=32
fac(3=12
elseif(modi==3then
fac(4=32
summ=summ+func(limit_up*7
integ=2*h*summ/45
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
func=x**2-5
programroot
iter=0
x,dx,guess_st,tolx,fold,exact,func
exact=sqrt(5.0d0
guess_st=1.0d0
dx=0.5
tolx=1.0d-8
x=guess_st
fold=func(x
dowhile(abs(dx>
tolx
iter=iter+1
x=x+dx
if(fold*func(x>
0.0then
cycle
x=x-dx
dx=dx/2
(I4,6f12.8"
iter,x,exact-xenddo
endprogramroot
5.2牛顿法
doubleprecisionfunctionfunc_prime(x
func_prime=2*x
endfunctionfunc_prime
x,x0,dx,guess_st,tolx,exact,func,func_prime
x0=x
x=x0-func(x0/func_prime(x0
dx=x-x0
iter,x,exact-x
5.3弦割法
x,x0,dx,guess_st,x3_st,xold,tolx,exact,func
xold=x0
if(iter==1then
x=x3_st
x=x0-func(x0*(x0-xold/(func(x0-func(xoldendif
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