New Sinc Methods of Numerical Analysis

This contributed volume honors the 80th birthday of Frank Stenger who established new Sinc methods in numerical analysis.The contributions, written independently from each other, show the new developments in numerical analysis in connection with Sinc methods and approximations of solutions for differential equations, boundary value problems, integral equations, integrals, linear transforms, eigenvalue problems, polynomial approximations, computations on polyhedra, and many applications. The approximation methods are exponentially converging compared with standard methods and save resources in computation. They are applicable in many fields of science including mathematics, physics, and engineering.The ideas discussed serve as a starting point in many different directions in numerical analysis research and applications which will lead to new and unprecedented results. This book will appeal to a wide readership, from students to specialized experts.

Introduces new exponentially convergent methods for solving multidimensional PDE, for indefinite integration and solution of indefinite convolution problems over finite or infinite intervals, for inverting Laplace transforms, and for inversion of Fourier transforms Presents new easy to apply and exponentially convergent methods of interpolation, quadrature and Hilbert transforms, over all intervals, finite, semi-infinite, infinite, or even arcs Includes a method of solution of Wiener-Hopf problems that works in all cases and enables circumvention of the popular factorization procedure that seldom works in applications Contains new methods of solving ODEs, PDEs, etc. problems over infinite regions as well as easy-to-apply methods for solving problems via use of polynomials

Inhalt
Part I Applications.- 1 Sinc-Gaussian Approach for Solving The Inverse Heat Conduction Problem.- 2 Poly-Sinc Collocation Method for Solving Coupled Burgers' Equations With a Large Reynolds number.- 3 Sinc Projection Solutions of Fredholm integral Equations.- 4 Lévy-Schrödinger Equation: Their eigenvalues and eigenfunctions using Sinc Methods.- 5 Application of Sinc on the Multi-Order Fractional Differential Equations.- 6 Election integrity audits to ensure election outcome accuracy .- 7 Numerical Solution of the Falkner-Skan Equation Arising in boundary layer Theory Using the sinc-collocation Method.- 8 Sinc Methods on Polyhedra.- Part II New Developments .- 9 Indenite integration operators Identities, and their Approximations.- 10 An Algorithm for Quadratic Minimization.- 11 An Overview of the Computation of the eigenvalues Using Sinc-Methods.- 12 Completely Monotonic Fredholm Determinants.- 13 The inuence of jumps on the sinc interpolant, and ways to overcome it.- 14 Construction of approximation formulas for analytic functions by mathematical optimization.- 15 LU Factorization of any Matrix.- Part III Frank Stenger's Work.- 16 Publications by, and about, Frank Stenger.