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CamiDiff.jl is a Julia package for one-dimensional finite-difference analysis.

Install

The package is installed using the Julia package manager

julia> using Pkg; Pkg.add("CamiDiff")

julia> using CamiDiff

Introduction

CamiDiff has been developed to analyze mathematical functions, provided by the user in tabulated form. The package is based on finite-difference analysis methods in one dimension.

Throughout the documentation $f(x)$ will be the 'function of interest' under investigation. In tabulated form we write $f[n]$. This form can be regarded as the result of the discretization of $f(x)$ on a Grid of $N$ points, addressable by the grid index $n = 1, ⋯ N$. The Grid can be linear (uniform) or non-linear as specified by a gridfunction - see Discretization.

The current implementation of CamiDiff was developed for real functions of a single variable. A set of four predefined gridfunctions is included in the package: 'exponential', 'truncated-exponential', 'linear' and 'polynomial'. These are restricted to the domain $[0, ∞)$. When applicable, we shall underline this restriction to the non-negative domain by using the variable $r$ rather than $x$, writing $f(r)$ rather than $f(x)$, with the implicit condition $r ≥ 0$.