Numerical solving of initial-value problems by R_bfbasis functions

Maximum entropy algorithm with inexact upper entropy bound based on Fup basis functions with compact support

“…If all moment equations in (7) for a new vector k kþ1 have values less than g 1 , then stop the procedure and set the current solution as a final solution (9). Otherwise, set k ¼ k þ 1 and go to step 2.…”

“…Finally, we need to check consequences of an inexact nature of our algorithm with respect to the upper entropy bound comparing entropy values for classic MaxEnt Algorithm and pdf in (9) or (16) and for FMEA and pdf in (20). In the first example (beta pdf), we firstly check the entropy values for basic algorithm with monomials and pdf (9) and algorithm with Chebyshev polynomials and pdf (16).…”

“…Gotovac and Kozulić [8] systemized the existing knowledge on atomic functions and presented the transformation of basis functions into a numerically applicable form. The application of Fup basis functions has been demonstrated in signal processing [14], for solving the integral Fredholm equations [13], in initial value problems [9], and in the collocation methods for boundary value problems [10]. Recently, Fup basis functions were applied to the Monte-Carlo methodology and stochastic processes of flow and transport in heterogeneous porous media [11].…”

Eksponencijalne atomske bazne funkcije : razvoj i primjena

“…Atomske bazne funkcije koriste se za rješavanje problema procesuiranja signala [33], [34], u analizi različitih problema strukturalne mehanike i matematičke fizike [1], [8], [9], [12], [13], [16], [26], [27], [28], [29], [30], [43], a zahvaljujući svojim svojstvima veoma uspješno se mogu primijeniti za rješavanje 1D i 2D problema [3], [10], [11], [24], [25]. Razvijena je i efikasna adaptivna Fup kolokacijska metoda koja je uspješno implementirana u problemima mehanike fluida i modeliranju rubno-početnih problema [14], [15], [17], [18], [19], [31], [32].…”

“…Dakle, funkcija dobije se konvolucijom beskonačnog broja algebarskih splineova nultog stupnja (3.6) sažetih na duljinu nosača 2 %9 s ordinatama veličine 2 9 kako je prikazano na crtežu 3.1. Prema tome je i nosač funkcije unija neizmjerno mnogo nosača članova iz konvolucije (3.5), a ipak je njegova duljina konačna, tj.…”