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| program Curs
implicit none
interface
subroutine threediagmatrix(C,Ans,n,Out)
integer n
real C(n),Ans(n),Out(n)
end subroutine
subroutine threediagsolve(A,B,C,Ans,n,Out)
integer n
real A(2:n),B(1:n-1),C(n),Ans(n),Out(n)
end subroutine threediagsolve
subroutine oddevensolve(C,F,size,vsize,n,Out)
integer size,vsize,n
real F(0:vsize,size),C(size,size),Out(0:vsize,size)
end subroutine oddevensolve
subroutine findC(C,l,k,sz,Out)
integer l,k,sz
real C(sz,sz),Out(sz,sz)
end subroutine findC
function findAlpha(l,k)
integer l,k
end function
real function k(x)
real x
end function
real function g1(x)
real x
end function
real function g2(x)
real x
end function
real function g3(x)
real x
end function
real function g4(x)
real x
end function
real function u(x,y)
real x,y
end function
real function func(x,y)
real x,y
end function
end interface
! Variables
integer, parameter :: length = 4
! number of y-values integer, parameter :: vlength = 4
! number of y-values real maxmodmaxmod
integer, parameter :: vlength = 4
real maxmod
integer i, j
real F(0:vlength, 0:length - 1), C(0:length - 1, 0:length - 1), Rr(0:vlength, 0:length - 1)
real hx,hy,x0,y0,xn,yn,hi
!initialization
x0 = 0
y0 = 0
xn = 4
yn = 4
hx = (xn - x0) / length
hy = (yn - y0) / vlength
C = 0
hi =1
F = 0
do i = 1,length - 2
C(i-1,i) = -(hy**2)/(hx**2)*k(x0 + (i - 0.5)*hx)
C(i,i) = (hy**2)/(hx**2)*k(x0 + (i - 0.5)*hx) + (hy**2)/(hx**2)*k(x0 + (i + 0.5)*hx) + 2
C(i+1,i) = -(hy**2)/(hx**2)*k(x0 + (i + 0.5)*hx)
enddo
C(length - 2,length - 1) = -(hy**2)/(hx**2)*k(xn - 1.5*hx)
C(length - 1, length - 1) = (hy**2)/(hx**2)*k(xn - 1.5*hx) + (hy**2)/(hx**2)*k(xn - 0.5*hx) + 2
do j = 1, vlength - 1
F(j,length - 1) = (hy**2) * func(xn - hx,y0 + j * hy) + (hy**2)/(hx**2) * g2(y0+j * hy) * k(xn - 0.5*hx)
enddo
C(0,0) = 2*((hy**2)/(hx**2) * k(x0 + 0.5*hx) + hi*hy/hx + 1)
C(1,0) = - 2*(hy**2)/(hx**2)*k(x0 + 0.5*hx)
do j = 1, vlength - 1
F(j,0) = (hy**2) * func(x0,y0 + j * hy) + 2*(hy**2)/(hx**2) * g1(y0+j * hy)
enddo
do j = 1,vlength - 1
do i = 1,length - 2
F(j,i) = (hy**2) * func(x0 + i*hx,y0 + j*hy)
enddo
enddo
print *, " "
do i = 0, length - 1
F(0,i) = g3(x0 + i*hx)
F(vlength,i) = g4(x0 + i*hx)
enddo
call oddevensolve(C,F,length,vlength,int(log(float(vlength))/log(2.0)),Rr) ! call of solving procedure
! finding error value maxmod = 0
do j = 1, vlength-1
do i = 1,length-2
!print *, "i = ",i," j = ",j
!print *, Rr(j,i) ," ----- ", u(x0 + i*hx,y0 + j*hy)
if (abs(Rr(j,i) - u(x0 + i*hx,y0 + j*hy)) > maxmod) then
maxmod = abs(Rr(j,i) - u(x0 + i*hx,y0 + j*hy))
endif
enddo
enddo
print *,"Max is ",maxmod
end program Curs
subroutine findC(C,l,k,sz,Out)
integer l,k,sz
real C(sz,sz),Out(sz,sz)
real Pi
real E(sz,sz)
integer i
Pi = 4*atan(1.0)
E = 0
do i = 1,sz
E(i,i) = 1
enddo
Out = C - E * 2*cos(((2*float(l) - 1.0) * Pi)/2**(float(k)+1.0))
end subroutine
function findAlpha(l,k)
real Pi
integer l,k
pi = 4*atan(1.0)
findAlpha = (((-1)**(float(l)+1.0))/(2**float(k)))*sin(((2*(l- 1.0) * Pi))/(2**(float(k)+1.0)))
! findAlpha = (((-1)**(float(l)+1.0))/(2**float(k)))*sin(((2*float(l- 1.0) * Pi)/(2**(float(k)+1.0))))
end function
subroutine oddevensolve(C,F,size,vsize,n,Out)
integer n
integer size,vsize
real F(0:vsize,size),P(vsize-1,size),C(0:size-1,0:size- 1),Fi(size),Psi(size),V(vsize,size),Y(0:vsize,size)
real Out(0:vsize,size)
real A(2:size),B(1:size-1),Cc(size),Tmp(size,size)
integer k,j,l
integer i
do i = 1,vsize-1
P(i,:) = F(i,:)
enddo
! straight walk
do k = 1, n - 1
do j = 2**k,vsize - 2**k,2**k
print *, j
Fi = P(j - 2**(k-1),:) + P(j + 2**(k-1),:)
do l = 1,2**(k-1)
call findC(C,l,k-1,size,Tmp)
call threediagmatrix(Tmp,Fi * findAlpha(l,k-1),size,V(l,:))
P(j,:) = P(j,:) + V(l,:)
enddo
P(j,:) = 0.5 * P(j,:)
enddo
enddo
! reverse walk Y(0,:) = F(0,:)
Y(vsize,:) = F(vsize,:)
do k = n,1,-1
do j = 2**(k-1),vsize - 2**(k-1),2**k
print *, j
Fi = Y(j - 2**(k-1),:) + Y(j + 2**(k-1),:)
Psi = P(j,:)
Y(j,:) = 0
do l = 1,2**(k-1)
call findC(C,l,k-1,size,Tmp)
call threediagmatrix(Tmp,Psi + Fi * findAlpha(l,k-1),size,V(l,:))
Y(j,:) = Y(j,:) + V(l,:)
enddo
enddo
enddo
Out = Y
end subroutine oddevensolve
subroutine threediagmatrix(C,Ans,n,Out)
integer n
real C(n,n),Ans(n),Out(n)
real A(2:n),B(1:n-1),CC(n)
integer i,j
do i = 1,n
do j = 1,n
if (i == j) then
Cc(j) = C(i,j)
else if (i - j == 1) then
B(j) = C(i,j)
else if(j - i == 1) then
A(j) = C(i,j)
endif
enddo
enddo
call threediagsolve(A,B,Cc,Ans,N,Out)
return
end subroutine
subroutine threediagsolve(A,B,C,Ans,n,Out)
!input parameters
integer n
real A(2:n),B(1:n-1),C(n),Ans(n),Out(n)
!work parameters
real alpha(2:n),beta(2:n),X(n)
!body of method alpha(2) = -B(1)/C(1)
beta(2) = ans(1)/C(1)
do i = 2,n-1
alpha(i+1) = (-B(i))/(A(i)*alpha(i) + C(i))
beta(i+1) = (ans(i)-A(i)*beta(i))/(A(i)*alpha(i) + C(i))
enddo
X(n) = (ans(n) - A(n)*beta(n))/(C(n)+A(n)*alpha(n))
do i = 1,n-1
X(n-i) = alpha(n-i+1)*X(n-i+1) + beta(n-i+1)
enddo
Out = X
end subroutine threediagsolve
real function k(x)
real x
k = x
end function
real function func(x,y)
real x,y
func = -4*x - 2
end function
real function g1(x)
real x
g1 = x**2
end function
real function g2(x)
real x
g2 = 16 + x**2
end function
real function g3(x)
real x
g3 = x**2
end function
real function g4(x)
real x
g4 = 16 + x**2
end function
real function u(x,y)
real x,y
u = x**2 + y**2
end function |
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Сообщение было отмечено Markontr как решение
