FUNCTION3

 !Program name: FUNCTION3

!Euler’s method for differential equation dy/dx=-xy

!The exact solution: y=exp(-x^2/2)

!y(n+1)= y(n)+h(-xy)

!Y(n+1) <=> X+h

 

real :: x, y, h, exact, error

integer :: i

func(x,y)=-x*y

 

h=0.01

y=1.  

do i=0,1

   x=i

   y=y+h*func(x,y)

   exact=exp((-(x+h)**2)/2)

   error=exact-y

   print *, i, x+h, y, exact, error

end do

stop

end

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