Geodesic
Solution of the Fredholm integral equation of the second kind using spline functions
Mathematica Applicanda, Tome 10 (1982) no. 19, pp. 15-21.

Voir la notice de l'article provenant de la source Annales Societatis Mathematicae Polonae Series

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.
DOI : 10.14708/ma.v10i19.1530
Classification : 45L05 (45B05 65R20)
Mots-clés : Theoretical approximation of solutions,Fredholm integral equations,Integral equations 
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     title = {Solution of the {Fredholm} integral equation of the second kind using spline functions},
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Zdzisław Jabłoński. Solution of the Fredholm integral equation of the second kind using spline functions. Mathematica Applicanda, Tome 10 (1982) no. 19, pp.  15-21. doi : 10.14708/ma.v10i19.1530. http://geodesic.mathdoc.fr/articles/10.14708/ma.v10i19.1530/

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