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

Mathematica Applicanda (1982)

- Volume: 10, Issue: 19
- ISSN: 1730-2668

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topZdzisław 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 -

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