Convergence and stability of a collocation method for the generalized airfoil equation

Fromme, J. A.; Golberg, Michael A.

doi:10.1016/0096-3003(81)90023-0

Cited by 16 publications

(7 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…When g(x) is smooth, numerical approaches such as collocation and Galerkin have been proposed and examined (see, for example, [2,3,8,10,20,22]); however the weighted L2 -convergence results presented are valid only if we assume that all the integrals involved in the numerical methods are evaluated exactly. The effect of numerical integration in the evaluation of the elements of the final linear system is still an open question.…”

Section: U~(t)ec[-1 1]mentioning

confidence: 98%

On the numerical resolution of the generalized airfoil equation with Possio kernel

Monegato

Lepora

1989

Numer. Math.

View full text Add to dashboard Cite

show abstract

Section: U~(t)ec[-1 1]mentioning

confidence: 98%

On the numerical resolution of the generalized airfoil equation with Possio kernel

Monegato

Lepora

1989

Numer. Math.

View full text Add to dashboard Cite

show abstract

“…There are four sequences of Chebyshev polynomials, they are called Chebyshev polynomials of first (T n ), second (P n ), third (V n ) and fourth (W n ) kinds. W. Gaustchi [21] named these last two sequences in this way, before they had been designated as airfoil polynomials (see, e.g., [19]). Their trigonometric definitions are…”

Section: The Four Families Of Chebyshev Polynomialsmentioning

confidence: 99%

On connection coefficients of some perturbed of arbitrary order of the Chebyshev polynomials of second kind

Rocha

2019

Journal of Difference Equations and Applications

View full text Add to dashboard Cite

Orthogonal polynomials satisfy a recurrence relation of order two, where appear two coefficients. If we modify one of these coefficients at a certain order, we obtain a perturbed orthogonal sequence. In this work we consider in this way some perturbed of Chebyshev polynomials of second kind and we deal with the problem of finding the connection coefficients that allow to write the perturbed sequence in terms of the original one and in terms of the canonical basis. From the connection relations obtained and from two other relations, we deduce some results about zeros and interception points of these perturbed polynomials. All the work is valid for arbitrary order of perturbation.

show abstract

“…The L2 con,vergence of the polynomial collocation method has been established in a series of papers by Golberg [8,11] and Fromme [7]. The question of uniform convergence of the polynomial collocation method has been considered by Miel [18] and Junghanns [14].…”

Section: Introductionmentioning

confidence: 98%

On the uniform convergence of a collocation method for a class of singular integral equations

Cuminato

1987

BIT

View full text Add to dashboard Cite

Abstract.We establish the uniform convergence of a collocation method for solving a class of singular integral equations. This method uses the Jacobi polynomials {P~"a~} as basis elements and the zeros of a Chebyshev polynomial of the first kind as collocation points. Uniform convergence is shown to hold under the weak assumption that the kernel and the right-hand side are H61der-continuous functions. Convergence rates are also given.

show abstract

Convergence and stability of a collocation method for the generalized airfoil equation

Cited by 16 publications

References 8 publications

On the numerical resolution of the generalized airfoil equation with Possio kernel

On the numerical resolution of the generalized airfoil equation with Possio kernel

On connection coefficients of some perturbed of arbitrary order of the Chebyshev polynomials of second kind

On the uniform convergence of a collocation method for a class of singular integral equations

Contact Info

Product

Resources

About