Numerical differentiation using finite differences

Choose a function:

	f(x) = x^7
	f(x) = 1/(1+25x^2)
	f(x) = sin(2*pi*x)
	f(x) = tanh(x)
	f(x) = exp(x)
	self defined function: Please type the evaluation program of your function here using FORTRAN rules. Your final statement must be fu= some expression you computed before or just here depending on x You may use the constants pi, e(=exp(1)), sqrt2(=1.414...), the integer variables i,j,k, the logicals bool1,bool2,bool3 and the double precision variables sum,h1,h2,h3,h4,y(100),z(100),a(100,100) which are all intialized with zero resp. .false. . The routine has the parameters x (double, input) and fu (double out). never change x!. first is a local integer and set 0 before calling the function the first time. You may use this in order to initialize some local data and set it 1 afterwards to avoid multiple such initialization. Your settings of the local variables are preserved during program execution. C**** it computes the truncated McLaurin series of sin(pi*x) multiplied C**** by exp(-pi*x^2) if ( first .ne. 0 ) goto 100 C**** now compute the 40 first Taylor coefficients of sin(pi*x) in y(.) y(1)=pi do 50 i=2,40 y(i)=-y(i-1)*pi**2/dble(2*(i-1)*(2*i-1)) 50 continue 100 continue first=1 fu=0.d0 do 200 i=40,1,-1 fu=fu+y(i)*x**(i+i-1) 200 continue fu=fu*dexp(-pi*x**2) You must observe JAKEF's restrictions here!

which method should be used?

	( f(x+h) - f(x) ) / h (forward difference)
	( f(x+h) - f(x-h) ) / 2h (symmetric 2nd order)
	Richardson extrapolation based on the symmetric 2nd order difference

the derivative is required at

Click on "evaluate", in order to submit your input.