Topic
Sinc numerical methods
About: Sinc numerical methods is a research topic. Over the lifetime, 22 publications have been published within this topic receiving 1428 citations.
Papers
Book•
24 Jun 1993
TL;DR: Sinc methods as mentioned in this paper are based on the Sinc function, a wavelet-like function replete with identities which yield approximations to all classes of computational problems, such as problems over finite, semi-infinite, or infinite domains, problems with singularities, and boundary layer problems.
Abstract: Many mathematicians, scientists, and engineers are familiar with the Fast Fourier Transform, a method based upon the Discrete Fourier Transform. Perhaps not so many mathematicians, scientists, and engineers recognize that the Discrete Fourier Transform is one of a family of symbolic formulae called Sinc methods. Sinc methods are based upon the Sinc function, a wavelet-like function replete with identities which yield approximations to all classes of computational problems. Such problems include problems over finite, semi-infinite, or infinite domains, problems with singularities, and boundary layer problems. Written by the principle authority on the subject, this book introduces Sinc methods to the world of computation. It serves as an excellent research sourcebook as well as a textbook which uses analytic functions to derive Sinc methods for the advanced numerical analysis and applied approximation theory classrooms. Problem sections and historical notes are included.
892 citations
Book•
2 Dec 2010
TL;DR: The text most notably provides a detailed exposition of the Sinc separation of variables method for numerically solving the full range of partial differential equations (PDEs) of interest to scientists and engineers.
Abstract: Handbook of Sinc Numerical Methods presents an ideal road map for handling general numeric problems Reflecting the authors advances with Sinc since 1995, the text most notably provides a detailed exposition of the Sinc separation of variables method for numerically solving the full range of partial differential equations (PDEs) of interest to scientists and engineers This new theory, which combines Sinc convolution with the boundary integral equation (IE) approach, makes for exponentially faster convergence to solutions of differential equations The basis for the approach is the Sinc method of approximating almost every type of operation stemming from calculus via easily computed matrices of very low dimension The CD-ROM of this handbook contains roughly 450 MATLAB programs corresponding to exponentially convergent numerical algorithms for solving nearly every computational problem of science and engineering While the book makes Sinc methods accessible to users wanting to bypass the complete theory, it also offers sufficient theoretical details for readers who do want a full working understanding of this exciting area of numerical analysis
179 citations
TL;DR: The use of conformal maps for the acceleration of convergence of the trapezoidal rule and Sinc numerical methods and the so-called Sinc-Pade approximants are used to provide approximate results.
Abstract: We investigate the use of conformal maps for the acceleration of convergence of the trapezoidal rule and Sinc numerical methods. The conformal map is a polynomial adjustment to the $\sinh$ map, and allows the treatment of a finite number of singularities in the complex plane. In the case where locations are unknown, the so-called Sinc-Pade approximants are used to provide approximate results. This adaptive method is shown to have almost the same convergence properties. We use the conformal maps to generate high-accuracy solutions to several challenging integrals, nonlinear waves, and multidimensional integrals.
15 citations
TL;DR: The goal here is to investigate the expected discounted dividend payments and the expected penalty-reward function in the compound Poisson risk model with a threshold dividend strategy and proportional investment.
14 citations
Posted Content•
TL;DR: In this paper, the authors investigated the use of conformal maps for the acceleration of convergence of the trapezoidal rule and Sinc numerical methods, and used them to generate high accuracy solutions to several challenging integrals, nonlinear waves, and multidimensional integrals.
Abstract: We investigate the use of conformal maps for the acceleration of convergence of the trapezoidal rule and Sinc numerical methods. The conformal map is a polynomial adjustment to the $\sinh$ map, and allows the treatment of a finite number of singularities in the complex plane. In the case where locations are unknown, the so-called Sinc-Pad\'e approximants are used to provide approximate results. This adaptive method is shown to have almost the same convergence properties. We use the conformal maps to generate high accuracy solutions to several challenging integrals, nonlinear waves, and multidimensional integrals.
10 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 2 |
| 2020 | 2 |
| 2015 | 2 |
| 2014 | 1 |
| 2013 | 5 |
| 2012 | 1 |