Differential program in fortran

Hello , I’m Sakura Ebi

In this article , I introduce the differential program of fortran.

In this program has a function of calculate the differential of \(f(x)\) at any position.

differential formula is bellow
\[
f'(x) = \frac{d}{dx} f(x)
\]

source-code of this processing is below

function DIF_F(fun,x)
implicit none
double precision fun,x,DIF_F,dx
 dx = 1.0E-8 
 dIF_F = (fun(x+dx)-fun(x))/dx
end function 

Terminal Output of below shows differential of \( f(x) = x^2\) at \(x = 0,1…5\)

To show above Output list,I made a test program below.

This function needs the external statement.

program test implicit none
external func
double precision x,func,DIF_F
print *, "x","f'(x)","2x","error"
x = 0.d0
print *, x,DIF_F(func,x),2*x,DIF_F(func,x)-2*x
x = 1.d0
print *, x,DIF_F(func,x),2*x,DIF_F(func,x)-2*x
x = 2.d0
print *, x,DIF_F(func,x),2*x,DIF_F(func,x)-2*x
x = 3.d0
print *, x,DIF_F(func,x),2*x,DIF_F(func,x)-2*x 
x = 4.d0
print *, x,DIF_F(func,x),2*x,DIF_F(func,x)-2*x
x = 5.d0
print *, x,DIF_F(func,x),2*x,DIF_F(func,x)-2*x 
end program

Thanks by Sakua Ebi

In Japanese
微分プログラム [fortran]