https://github.com/0samuraie/centraldiff.jl
Higher-order central finite difference scheme
https://github.com/0samuraie/centraldiff.jl
central-difference discrete julia
Last synced: about 1 year ago
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Higher-order central finite difference scheme
- Host: GitHub
- URL: https://github.com/0samuraie/centraldiff.jl
- Owner: 0samuraiE
- License: mit
- Created: 2024-07-27T16:54:39.000Z (almost 2 years ago)
- Default Branch: master
- Last Pushed: 2024-11-18T18:16:20.000Z (over 1 year ago)
- Last Synced: 2025-03-24T08:55:10.443Z (over 1 year ago)
- Topics: central-difference, discrete, julia
- Language: Julia
- Homepage:
- Size: 226 KB
- Stars: 2
- Watchers: 1
- Forks: 1
- Open Issues: 1
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
# CentralDiff.jl
*Central difference in Julia*
[](https://0samuraiE.github.io/CentralDiff.jl/stable/)
[](https://0samuraiE.github.io/CentralDiff.jl/dev/)
[](https://github.com/0samuraiE/CentralDiff.jl/actions/workflows/CI.yml?query=branch%3Amaster)
[](https://codecov.io/gh/0samuraiE/CentralDiff.jl)
CentralDiff.jl is a Julia module for performing central difference on multi-dimensional data. It provides tools to compute numerical derivatives and supports higher-order finite differences.
## Features
- Compute finite differences up to order 20 with zero-cost abstraction.
- Support for multi-dimensional arrays.
- Includes a Simple module for usage that does not require consistency.
## Installation
CentralDiff.jl can be installed with the Julia package manager. From the Julia REPL, type `]` to
enter the Pkg REPL mode and run:
```
pkg> add https://github.com/0samuraiE/CentralDiff.jl.git
```
## Usage
```julia
julia> using CentralDiff
julia> f(x) = x^2;
julia> fc(Order(4), f.(1:4)) # The analytical solution is 2.5^2=6.25
6.25
julia> dfdxc(Order(6), f.(1:6), 1) # The analytical solution is 2*3.5=7.0
7.0
julia> dfdx(Order(4), f.(1:7), 1) # The analytical solution is 2*4.0=8.0
7.999999999999999
julia> d2fdx(Order(4), f.(1:7), 1) # The analytical solution is 2
1.999999999999998
julia> Simple.dfdx(Order(4), f.(1:5), 1) # The analytical solution is 2*3.0=6.0
5.999999999999999
julia> Simple.d2fdx(Order(4), f.(1:5), 1) # The analytical solution is 2
1.9999999999999991
```
## Advanced Usage
```julia
julia> g̃((x, y, z)) = sin(x) * sin(y) * sin(z);
dg̃dx((x, y, z)) = cos(x) * sin(y) * sin(z);
dg̃dy((x, y, z)) = sin(x) * cos(y) * sin(z);
dg̃dz((x, y, z)) = sin(x) * sin(y) * cos(z);
d2g̃dx((x, y, z)) = -sin(x) * sin(y) * sin(z);
d2g̃dy((x, y, z)) = -sin(x) * sin(y) * sin(z);
d2g̃dz((x, y, z)) = -sin(x) * sin(y) * sin(z);
X = Y = Z = range(0, 2π; length=64);
dx = dy = dz = step(X); dxi = dyi = dzi = 1 / dx;
MESH = collect(Iterators.product(X, Y, Z));
G = g̃.(MESH);
I0 = CartesianIndex(8, 8, 8);
x0, y0, z0 = MESH[I0];
julia> fc(Order(2), XAxis(), G, I0) - g̃((x0+dx/2, y0, z0))
-0.0003493436613384304
julia> dfdxc(Order(4), YAxis(), G, I0, dyi) - dg̃dy((x0, y0+dy/2, z0))
-1.4038190432330566e-7
julia> dfdx(Order(6), ZAxis(), G, I0, dzi) - dg̃dz((x0, y0, z0))
-1.7355242798444692e-9
julia> d2fdx(Order(8), ZAxis(), G, I0, dzi) - d2g̃dz((x0, y0, z0))
6.298850330210826e-13
julia> Simple.dfdx(Order(10), XAxis(), G, I0, dxi) - dg̃dx((x0, y0, z0))
-1.1435297153639112e-14
julia> Simple.d2fdx(Order(12), XAxis(), G, I0, dxi) - d2g̃dx((x0, y0, z0))
-1.27675647831893e-15
```