Finite, Fortran - rextester

Finite

Program Finite_diffenence_method
Implicit None
     Real::aa=0.0,bb=atan(1.0),h,w(0:15),p,q,r,x,ex,&
          a(15),b(15),d(15),l(15),u(15),z(15),c(15)
    Real::u1(100,0:100),v(100,0:100),w1(100,0:100),k(4,2),g(4,2)
    integer::n=13,i

h=(bb-aa)/(n+1)

CALL FDM(x,w)

Write(*,*)"         x             exact           finite            "
    Write(*,*)"_______________________________"
     Do i=0,n+1
        x=aa+i*h
        Write(*,22)x,ex(x),w(i)
    end do

22 FORMAT(4(2X,f13.6))

End Program

Subroutine FDM(x,w)
Implicit none
    Real::aa=0.0,bb=atan(1.0),h,w(0:15),p,q,r,x,ex,&
          a(15),b(15),d(15),l(15),u(15),z(15),c(15)
    integer::n=13,i

w(0)=1.0
    w(n+1)=2.0
    h=(bb-aa)/(n+1)

x=aa+h

a(1)=2+(h**2)*q(x)
    b(1)=-1+(h/2.)*p(x)
    d(1)=-(h**2)*r(x)+(1+(h/2.)*p(x))*w(0)

do i=2,n-1
        x=aa+i*h
        a(i)=2+(h**2*q(x))
        b(i)=-1+(h/2.)*p(x)
        c(i)=-1-(h/2.)*p(x)
        d(i)=-(h**2)*r(x)
    end do

x=bb-h
    a(n)=2+(h**2)*q(x)

c(n)=-1-(h/2.)*p(x)
    d(n)=-(h**2)*r(x)+(1-(h/2.)*p(x))    *w(n+1)

l(1)=a(1)
    u(1)=b(1)/a(1)
    z(1)=d(1)/l(1)

do i=2,n-1
    l(i)=a(i)-c(i)*u(i-1)
    u(i)=b(i)/l(i)
    z(i)=(d(i)-c(i)*z(i-1))/l(i)
end do

l(n)=a(n)-c(n)*u(n-1)
    z(n)=(d(n)-c(n)*z(n-1))/l(n)

w(n)=z(n)

do i=n-1,1,-1
        w(i)=z(i)-u(i)*w(i+1)
        end do

End Subroutine

Real function p(x)
    implicit none
    real::x
    p=-2.0/x
    return
    end function p

Real function q(x)
    implicit none
    real::x
    q=2.0/(X**2.0)
    return
    end function q

Real function r(x)
    implicit none
    real::x
    r=SIN(LOG(x))/(x**2.0)
    return
    end function r

Real function ex(x)
    implicit none
    real::x
    ex=-0.03920701320*x+(1.1392070132)*(1.0/x**2.0)-(3.0/10.0)*(SIN(LOG(x)))-(1.0/10.0)*(COS(LOG(x)))
    return
    end function ex


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