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FiniteDifferenceDerivatives

Compute derivatives using finite difference of arbitrary order

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FiniteDifferenceDerivatives

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Usage example

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.

TODO

  • Add specialized functions for symmetric finite differences

First Commit

10/15/2014

Last Touched

over 5 years ago

Commits

21 commits