Function fdd!(df,f,x,k,n) computes the k-th derivative of f on a
nonuniformly spaced mesh x using n-point stencli. The result is
written to the array df.
using FiniteDifferenceDerivatives
x = linspace(0,1,11)
f = x.^2
df = zero(f)
fdd!(df,f,x,1,3) # Compute the first derivative using three point stencil
You can also use fdd, which allocates and returns the df
df = fdd(f,x,1,3)
It is also possible to compute the differentiation matrix with
D1 = fddmatrix(x,1,3)
using Base.Test
@test_approx_eq(D1*f,df)
To compute the second derivative at point x0 given the function values f at
mesh points x you can call
x = linspace(0,1,11)
fddat(x.^2,x,2,0.5)
It is also possible to compute the derivative outside the interval
[0,1] but this might generate large errors for nonpolynomial
functions f
fddat(x.^2,x,1,2.0) # returns 4.000000002793968
fddat(1./(1.+x.^2),x,1,2.0) # returns 17.610649429727346
the true first derivative of 1/(1+x^2) at x=2.0 is -0.16.
- Add specialized functions for symmetric finite differences