Solution of the Fredholm integral equation of the second kind using spline functions

Zdzisław Jabłoński. "Solution of the Fredholm integral equation of the second kind using spline functions." Mathematica Applicanda 10.19 (1982): null. <http://eudml.org/doc/293420>.

@article{ZdzisławJabłoński1982,
abstract = {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.},
author = {Zdzisław Jabłoński},
journal = {Mathematica Applicanda},
keywords = {Theoretical approximation of solutions,Fredholm integral equations,Integral equations},
language = {eng},
number = {19},
pages = {null},
title = {Solution of the Fredholm integral equation of the second kind using spline functions},
url = {http://eudml.org/doc/293420},
volume = {10},
year = {1982},
}

TY - JOUR
AU - Zdzisław Jabłoński
TI - Solution of the Fredholm integral equation of the second kind using spline functions
JO - Mathematica Applicanda
PY - 1982
VL - 10
IS - 19
SP - null
AB - 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.
LA - eng
KW - Theoretical approximation of solutions,Fredholm integral equations,Integral equations
UR - http://eudml.org/doc/293420
ER -