LyonCalcul.jl
Documentation for LyonCalcul.jl
LyonCalcul.Advection — TypeAdvection(n, p, delta)
n :: Number of points.
p :: Spline degree.
delta :: space size step.LyonCalcul.Advection — Methodadvection! = Advection( n, p, delta)
advection!( f, alpha )
Create a function to compute the interpolating spline
of degree p of odd
degree of a 1D function f on a periodic uniform mesh, at
all points x after a displacement alpha.
Input f type is Vector{Float64} and is updated inplace.LyonCalcul.bspline — Methodbspline(p, j, x)Return the value at x in [0,1[ of the B-spline with integer nodes of degree p with support starting at j. Implemented recursively using the De Boor's Algorithm
\[B_{i,0}(x) := \left\{
\begin{matrix}
1 & \mathrm{if} \quad t_i ≤ x < t_{i+1} \\
0 & \mathrm{otherwise}
\end{matrix}
\right.\]
\[B_{i,p}(x) := \frac{x - t_i}{t_{i+p} - t_i} B_{i,p-1}(x)
+ \frac{t_{i+p+1} - x}{t_{i+p+1} - t_{i+1}} B_{i+1,p-1}(x).\]