WebOct 1, 2010 · Based on the analysis, a class of collocation-type methods are proposed for solving integral equations with Hadamard finite-part kernels. The accuracy of the collocation method is the same as the accuracy of the proposed even-order Newton―Cotes rules. Several numerical examples are provided to illustrate the theoretical analysis. WebIn this paper, we develop a method for evaluating one dimensional singular integrals (weakly, strongly, and hyper-singular) that converge in the sense of Cauchy principal value and Hadamard finite part integrals. A proof of convergence of this method is also provided.
[2012.01943] Finite-Part Integration in the Presence of …
WebThis brief report studies conditions to ensure the nonexistence of finite-time stable equilibria in a class of systems that are described by means of nonlinear integral equations, … WebMay 26, 2024 · 3. Appendix: The Hadamard Finite Part. The concept of the finite part of a (possibly divergent) integral was introduced by Hadamard as a convenient way to express solutions of differential equations. He showed that this finite part of an integral (which coincides with the usual value if the integral is convergent) can be combined and ... ovo alpino americanas
[1805.01734] Finite-Part Integration of the Generalized Stieltjes ...
WebMay 1, 1989 · The simple remark that Kutt's Gaussian quadrature rule for the computation of divergent integrals of the form (with λ ⩽ - 1), defined in the sense of finite-part integrals, coincides with the Gauss-Jacobi quadrature rule and the corresponding orthogonal polynomials with shifted Jacobi polynomials is made. This remark is based on the well … WebApr 8, 2024 · This paper is devoted to investigating the relationship between Riesz, Riesz–Caputo, Hilfer fractional derivatives and the corresponding finite part integrals in Hadamard sense. WebSep 16, 2024 · This paper is devoted to investigating the relation between Hadamard-type fractional derivatives and finite part integrals in Hadamard sense; that is to say, the Hadamardtype fractional derivative ... イブニクル2