Wszystkie pola: Jabłoński, Zdzisław - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: The solution of the first interior Fouriers problem with application of spline functions
Autorzy:: Jabłoński, Zdzisław
Powiązania:: https://bibliotekanauki.pl/articles/748265.pdf
Data publikacji:: 1985
Wydawca:: Polskie Towarzystwo Matematyczne
Tematy:: Integral equations, Numerical analysis
Opis:: .
Volterra's integral equation (which arises from the first interior Fourier's problem) by spline functions of the cubic polinomials. Namely, the approximate solution of this equation is represented in the form of linear combination of spline functions, which are forming the distributions of unity within the segments [0, 2] and [0,t] respectively. The error of approximation we associate on natural way with perfectin of considered distributions of unity. The estimation of the error is given at the end of the paper.
Źródło:: Mathematica Applicanda; 1985, 13, 25
1730-2668
2299-4009
Pojawia się w:: Mathematica Applicanda
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: Solution of the Fredholm integral equation of the second kind using spline functions
Autorzy:: Jabłoński, Zdzisław
Powiązania:: https://bibliotekanauki.pl/articles/748607.pdf
Data publikacji:: 1982
Wydawca:: Polskie Towarzystwo Matematyczne
Tematy:: Theoretical approximation of solutions,Fredholm integral equations,Integral equations
Opis:: .
The author presents a polynomial spline function method for solution of the linear Fredholm integral equation f(s)+K1f(s)=φ(s), where K1f(s)=∫CK(s,t)f(t)dt, τ∈[0,2π], and C is a Jordan curve. The method is as follows: The approximate equation for the function fδ(s) is (1) fδ+K1δfδ=φ, where K1δ=K1Tδ, and (2) Tδf(t)=∑n−1i=0f(ti)Wi4(t)Ni1(t). Here Wi4(t) is a spline function, i.e., a 3rd degree polynomial, and Ni1(t)=1 for t∈[ti,ti+1) and Ni1(t)=0 for t∉[ti,ti+1). The substitution of (2) into (1) leads to the equation fδ(s)+∑n−1i=0fδ(ti)K1ei4(s)=φ(s), where ei4(t)=Wi4(t)Ni1(t), i=0,⋯,n−1. The coefficients satisfy the equations fδ(tl)+∑i=0n−1fδ(ti)K1ei4(tl)=φ(tl),l=0,⋯,n−1. The author gives an estimate for ∥fδ−f∥C, and ends the article with an example.
Źródło:: Mathematica Applicanda; 1982, 10, 19
1730-2668
2299-4009
Pojawia się w:: Mathematica Applicanda
Dostawca treści:: Biblioteka Nauki