Weighted Polynomial Approximation and Numerical Methods for Integral Equations
Springer International Publishing (Verlag)
978-3-030-77496-7 (ISBN)
The text focusses on interpolation and quadrature processes for functions defined on bounded and unbounded intervals and having certain singularities at the endpoints of the interval, as well as on numerical methods for Fredholm integral equations of first and second kind with smooth and weakly singular kernel functions, linear and nonlinear Cauchy singular integral equations, and hypersingular integral equations.
The book includes both classic and very recent results and will appeal to graduate students and researchers who want to learn about the approximation of functions and the numerical solution of operator equations, in particular integral equations.
lt;b>Peter Junghanns is Professor Emeritus at the Mathematics Department of the Technical University of Chemnitz, Germany, where he got his habilitation in 1984. His field of specialization includes analysis and numerical methods for operator equations, in particular integral equations.
Giuseppe Mastroianni is emeritus professor of Numerical Analysis at the University of Basilicata (Italy) since 2013, where he had been full professor since 1987. In 1971 he graduated with honors in Mathematics at the University of Naples "Federico II", where he began his academic career. His scientific interests are focused on polynomial approximation, positive operators, mechanical quadrature and numerical treatment of integral equations. His research contributions have been published in numerous papers as well as the monographs "Interpolation processes. Basic theory and applications" (with G.V. Milovanovic) and "Elementi di teoria dell'approssimazione polinomiale" (with M.C. De Bonis and I. Notarangelo).
Incoronata Notarangelo is assistant professor in Numerical Analysis at the University of Turin (Italy) since 2019. After graduating with honors in Mathematics, she received a PhD in Mathematics from the University of Basilicata (in cooperation with the University of Szeged, Hungary) in 2010. Her scientific interests include polynomial approximation, quadrature rules and numerical methods for integral equations. Her research contributions appeared in various papers as well as the monograph "Elementi di teoria dell'approssimazione polinomiale" (with M.C. De Bonis and G. Mastroianni).
- Introduction. - Basics from Linear and Nonlinear Functional Analysis. - Weighted Polynomial Approximation and Quadrature Rules on (-1, 1). - Weighted Polynomial Approximation and Quadrature Rules on Unbounded Intervals. - Mapping Properties of Some Classes of Integral Operators. - Numerical Methods for Fredholm Integral Equations. - Collocation and Collocation-Quadrature Methods for Strongly Singular Integral Equations. - Applications. - Hints and Answers to the Exercises. - Equalities and Inequalities.
"It is worthy to highlight the good structure of the book. On the one hand, the book is self-contained so deeply recommended for academic purposes and on the other hand, it is of unbounded interest for many researchers in applied and pure mathematics. Moreover, the book which are very helpful for readers. Finally, the authors also provide lists of exercises in every single chapter, very helpful also for the right understanding of the contents given." (Eduardo Cuesta, zbMATH 1533.65004, 2024)
| Erscheinungsdatum | 13.08.2021 |
|---|---|
| Reihe/Serie | Pathways in Mathematics |
| Zusatzinfo | X, 658 p. 5 illus., 3 illus. in color. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 1160 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Schlagworte | Collocation method • Collocation-quadrature Method • Fredholm Integral Equations • Gaussian Rules • Hyper Singular Integral Equations • Strongly Singular Integral Equations • Weakly Singular Integral Equations • Weighted Polynomial Approximation |
| ISBN-10 | 3-030-77496-1 / 3030774961 |
| ISBN-13 | 978-3-030-77496-7 / 9783030774967 |
| Zustand | Neuware |
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