33 research outputs found
Quadrature methods for integro-differential equations of Prandtl's type in weighted spaces of continuous functions
The paper deals with the approximate solution of integro-differential
equations of Prandtl's type. Quadrature methods involving ``optimal'' Lagrange
interpolation processes are proposed and conditions under which they are stable
and convergent in suitable weighted spaces of continuous functions are proved.
The efficiency of the method has been tested by some numerical experiments,
some of them including comparisons with other numerical procedures. In
particular, as an application, we have implemented the method for solving
Prandtl's equation governing the circulation air flow along the contour of a
plane wing profile, in the case of elliptic or rectangular wing-shape.Comment: 34 page
The numerical solution of Cauchy singular integral equations with additional fixed singularities
In this paper we propose a quadrature method for the numerical solution of Cauchy singular integral
equations with additional fixed singularities. The unknown function is approximated by a weighted
polynomial which is the solution of a finite dimensional equation obtained discretizing the involved
integral operators by means of a Gauss-Jacobi quadrature rule. Stability and convergence results for the
proposed procedure are proved. Moreover, we prove that the linear systems one has to solve, in order to
determine the unknown coefficients of the approximate solutions, are well conditioned. The efficiency of
the proposed method is shown through some numerical examples
Approximation of Hilbert and Hadamard transforms on (0, +∞)
The authors propose a numerical method for computing Hilbert and Hadamard transforms on (0, +∞) by a simultaneous approximation process involving a suitable Lagrange polynomial of degree s and “truncated” Gaussian rule of order m, with s<
Numerical Treatment of a class of systems of Fredholm integral equations on the real line
In this paper the authors propose a Nystrom method based on a ``truncated" Gaussian rule to solve systems of Fredholm integral equations on the real line. They prove that it is stable and convergent and that the matrices of the solved linear systems are well-conditioned. Moreover, they give error estimates in weighted uniform norm and show some numerical tests
Remarks on two integral operators and numerical methods for CSIE
In this paper the author extends the mapping properties of some singular integral operators in Zygmund spaces equipped with uniform norm. As by-product quadrature methods for solving CSIE having index and are proposed. Their stability and convergence are proved and error estimates in Zygmund norm are given. Some numerical tests are also shown
Nyström method for systems of integral equations on the real semiaxis
In this paper, the authors introduce a Nystrom method for solving systems of Fredholm integral equations
on the real semiaxis. They prove that the method is stable and convergent. Moreover, they show some
numerical tests that confirm the error estimates. Finally, they discuss a specific application to an inverse
scattering problem for the Schrodinger equation