olekravchenko

FTup[x_, elemProd_] := Product[Sinc[x 2^-k], {k, 1, elemProd}]
up[x_, elemProd_, elemSum_] := 
 If[-1 <= x && x <= 1, 
  0.5 + Sum[FTup[k \[Pi], elemProd] Cos[\[Pi] k x], {k, 1, elemSum}], 
  0]


elemProd = 4;
elemSum = 20;
Plot[{up[x, elemProd, elemSum]}, {x, -1 - 0.025, 1 + 0.025}, 

olekravchenko

(*Fabius Function*)
Fb[x_] := up[x - 1, 5, 30]
(*Statement Function*)
GFb[a1_, a2_, b_] := a2 - a1 + b (Fb[a1/b] - Fb[a2/b]) // Evaluate
(*Samples*)
GFb[2, 13, 30];
GFb[2, 7, 18];

(*Search*)
tbl = Table[{b, GFb[2, 9, b]}, {b, 15, 25, 1}];

olekravchenko

(*FDE:
f'(x) = 2.25*(3f(3x) - 2f(3x-1) - f(3x-2)),
supp f = [0,1]
*)
(*Fourier Transform of f(x)*)
fFt[\[Omega]_] := 
 Product[1/4 (3 - 2 Exp[-I \[Omega] 3^-n] - Exp[-2 I \[Omega] 3^-n])/(
   I \[Omega] 3^-n), {n, 1, 4}]
(*Fourier Series of f(x)*)
f[x_] := 0.5 + 

olekravchenko

(*Exponential atomic function*)

(*Fourier Transform*)
Sinch[x_] := If[x == 0, 0, Sinh[x]/x];
FTeup[a_, t_] := 
 Product[(Sinch[Log[a]/2])^-1 Sinch[Log[a]/2 - I t /2^j], {j, 1, 4}];
 
 (*Eup AF via Fourier Series*)
 eup[a_, x_] := 
 If[-1 <= x <= 1, 

olekravchenko

(*
Author: Oleg Kravchenko;
Date: 18/6/16;
*)

ClearAll["Global`*"]
(*eup(x) function via convolution*)

eUP[k_, x_] := 2^k UnitBox[2^k x] Exp[x]
c1eUP[x_] := Convolve[eUP[0, s], eUP[1, s], s, x] // Evaluate

olekravchenko

f[x_] := 1/2 - (4/\[Pi]) Arg[QPochhammer[I (2 x - 1)]]
upFT[t_] := Product[Sinc[t 2^-k], {k, 1, 5}]
up[x_] := 1/2 + Sum[Cos[\[Pi] k x] upFT[\[Pi] k], {k, 1, 25}]

Column@{
  Plot[{up[x - 1], f[x]}, {x, 0, 1}, PlotStyle -> Thick, 
   ImageSize -> 450],
  Plot[Abs@{up[x - 1] - f[x]}, {x, 0, 1}, PlotStyle -> Thick, 
   ImageSize -> 450]
  }

olekravchenko

from sympy import *
#from sympy import Symbol, solve
from sympy.solvers.solveset import linsolve

# Set symbolic parameters
x, a, b, c, d, h, ui, ui1, gi, gi1 = symbols('x, a, b, c, d, h, ui, ui1, gi, gi1')
# Set interpolation polynomials
f = a + b*x + c*x**2 + d*x**3
df = f.diff(x)
# Set constrains

olekravchenko

B3[x_] := BSplineBasis[3, 0.25 (x + 2)]
FTfupn[x_, n_, elemProd_] := 
 Sinc[x/2]^(n + 1) Product[Sinc[x 2^-i], {i, 2, elemProd}]
fupn[x_, n_, elemProd_, elemSum_] := 
 If[-((n + 2)/2) <= x && x <= (n + 2)/2, 
  2/(n + 2) (0.5 + 
     Sum[FTfupn[ (2 k \[Pi])/(n + 2), n, 
        elemProd] Cos[(2 k \[Pi])/(n + 2) x], {k, 1, elemSum}]), 0]

Plot[{B3[x], fupn[x, 2, 4, 15]}, {x, -2, 2}, 

olekravchenko

upFt[t_, n_] := Product[Sinc[t 2^-k], {k, 1, n}]

Plot[{Sinc[2 \[Pi] t], upFt[2 \[Pi] t, 1], upFt[2 \[Pi] t, 2], 
  Cos[2 \[Pi] t]}, {t, -3.05, 3.05}, PlotRange -> All, 
 PlotStyle -> Thick,
 PlotLegends -> {"sinc(2\[Pi]t)", "sinc(\[Pi]t)", 
   "sinc(\[Pi]t)sinc(\[Pi]t/2)", "cos(x)"},
 ImageSize -> Large]

olekravchenko

    program gdns2s_strat_new
    use omp_lib
    parameter (ni=998)
    parameter (nj=1250)
    !implicit double precision (a-h,o-z)

    real (kind=8), allocatable, dimension(:)    ::  x, y, ylt, roaxe, paxe
    real (kind=8), allocatable, dimension(:,:)  ::  ro, u, v, es, rox, ux, vx, esx, roy, uy, vy, esy, dksi