1,721,052 research outputs found
Numerical solution of a singular integral equation with Cauchy kernel in the plane contact problem
No full textAbstract: This paper describes a collocation method for solving numerically a singular integral equation with Cauchy and Volterra operators, associated with a proper constraint condition. The numerical method is based on the transformation of the given integral problem into a hypersingular integral equation and then applying a collocation method to solve the latter equation. Convergence of the resulting method is then discussed, and optimal convergence rates for the collocation and discrete collocation methods are given in suitable weighted Sobolev spaces. Numerical examples are solved using the proposed numerical technique
Studio modellistico dei fenomeni di emissione e dispersione di sostanze inquinanti prodotte dal traffico autoveicolare in un'area urbana
No full textSome remarks on the numerical computation of integrals on an unbounded interval
No full textAbstract: An account of the error and the convergence theory is given for Gauss-Laguerre and Gauss-Radau-Laguerre quadrature formulae. We develop also truncated models of the original Gauss rules to compute integrals extended over the positive real axis. Numerical examples confirming the theoretical results are given comparing these rules among themselves and with different quadrature formulae proposed by other authors (Evans, Int. J. Comput. Math. 82:721730, 2005; Gautschi, BIT 31:438446, 1991)
Lagrange interpolation with constraints on the real line
No full textWe investigate the uniform convergence of Lagrange interpolation at the zeros of the orthogonal polynomials with respect to a Freud-type weight in the presence of constraints. We show that by a simple procedure it is always possible to transform the matrices of these zeros into matrices such that the corresponding Lagrange interpolating polynomial with re- spect to the given constraints well approximates a given function. This procedure was, at ̄rst, successfully introduced for the polynomial inter- polation with constraints on bounded intervals [1]. For this procedure we obtain the same results obtained in [10], where only the zeros of the orthogonal polynomials are used
Convergence and stability of a new quadrature rule for evaluating Hilbert transform
No full textAbstract: The importance of singular integral transforms, coming from their
many applications, justifies some interest in their numerical approximation.
Here we propose a stable and convergent algorithm to evaluate such transforms
on the real line. Numerical examples confirming the theoretical results
are given
Numerical solution of a hypersingular integral equation arising in a solid circular plate problem
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