Some numerical methods for second-kind Fredholm integral equations on the real semiaxis

Mastroianni, G.; Milovanović, Gradimir V.

doi:10.1093/imanum/drn056

Cited by 36 publications

(38 citation statements)

References 5 publications

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“…In this section we will discuss the convergence and the stability of the previous rules. About the formula (7), recently it was proved in [11] that…”

Section: Resultsmentioning

confidence: 99%

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Some quadrature formulae with nonstandard weights

Mastroianni

2010

Journal of Computational and Applied Mathematics

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“…In this section we will discuss the convergence and the stability of the previous rules. About the formula (7), recently it was proved in [11] that…”

Section: Resultsmentioning

confidence: 99%

“…We remark that, by an argument in [6], it is easy to prove that (11) does not hold if in (7) j is replaced by m, i.e. using the ordinary Gaussian rule.…”

Section: Resultsmentioning

confidence: 99%

Some quadrature formulae with nonstandard weights

Mastroianni

2010

Journal of Computational and Applied Mathematics

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“…the first variable x) evaluated at x k . Under conditions (5) if g, Kf ∈ Z s , s>0, it was proved (see [5, Theorem 2.1]) that the sequence of equations (6) has the unique solutions f n ∈ P n−1 , n = 1, 2, . .…”

Section: Integral Equations Onmentioning

confidence: 99%

Well‐conditioned matrices for numerical treatment of Fredholm integral equations of the second kind

Mastroianni

Milovanović

2009

Numerical Linear Algebra App

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SUMMARYIn the cases A =[−1, 1] and A =[0, +∞), with w(x) = (1− x) (1+ x) , , >−1, and w(x) = x e −x , >−1, > 1 2 , respectively, in this paper we consider the corresponding Fredholm integral equations of the second kindin the spaces of continuous functions equipped with certain uniform weighted norms. Assuming the continuity of the kernel k(x, y) we use Nyström methods and prove the stability, the convergence and the well conditioning of the corresponding matrices. The last property is derived only from the continuity of the kernel and not from its special form. Error estimates and numerical tests are also included.

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“…Let us note that the polynomialL m (w, f ) has a good behavior in [0, θa m ], with 0 < θ < 1, as it was shown in [12] for β = 1. For the second norm, it was proved in [7] that sup fu ∞ =1 L * * m+1 (w, f )u ∞ C log m under certain assumptions on the parameters α, γ, λ. The order log m cannot be improved [16].…”

Section: Laurita and G Mastroiannimentioning

confidence: 99%