599,633 Result(s)

Book

Book Series
Applied Mathematical Sciences
2020欧洲杯体育官方网站Volume 1 / 1971 to Volume 203 / 2021

2020欧洲杯体育官方网站 Chapter
The Matrix Schrödinger Equation and the Characterization of the Scattering Data
2020欧洲杯体育官方网站 In this chapter we describe the basic ingredients of the direct and inverse scattering problems for the matrix Schrödinger equation on the half line with the general selfadjoint boundary condition. We show ho...

2020欧洲杯体育官方网站 Chapter
Direct Scattering II
In this chapter the scattering process is described physically and mathematically, and the definition of the scattering operator is provided in terms of the wave operators introduced by Møller. The role of the...

2020欧洲杯体育官方网站 Chapter
Some Explicit Examples
In this chapter we illustrate the theory presented earlier via explicitly solved examples. It is shown how the Marchenko integral equation can yield explicitly solved examples when its kernel contains a matrix...

2020欧洲杯体育官方网站 Chapter
Introduction
In this introductory chapter the goals of the monograph are described, the contents of the remaining chapters and Appendix A are outlined, and the relevant general refer...

2020欧洲杯体育官方网站 Chapter
Direct Scattering I
2020欧洲杯体育官方网站 In this chapter we present the solution to the direct scattering problem for the halfline matrix Schrödinger equation using an input data set consisting of a matrix potential and a selfadjoint boundary condi...

2020欧洲杯体育官方网站 Chapter
Inverse Scattering
In this chapter we analyze the inverse scattering problem of recovery of the corresponding input data set D in the Faddeev class from a scattering data set S in the Marchenko class. We discuss the nonuniqueness a...

Journal
Japanese Journal of Mathematics
Volume 1 / 2006  Volume 15 / 2020

2020欧洲杯体育官方网站 Journal
Communications on Applied Mathematics and Computation
2020欧洲杯体育官方网站Volume 1 / 2019  Volume 2 / 2020

2020欧洲杯体育官方网站 Article
Open AccessA Multiphysics Methodology for Four States of Matter
We propose a numerical methodology for the simultaneous numerical simulation of four states of matter: gas, liquid, elastoplastic solids, and plasma. The distinct, interacting physical processes are described ...

Article
My Way: A Computational Autobiography
2020欧洲杯体育官方网站 In this paper, the author recounts his fortyyear plus struggle to find a sound basis for understanding the computational fluid dynamics of compressible flow.

Article
Rank and duality in representation theory
2020欧洲杯体育官方网站 There is both theoretical and numerical evidence that the set of irreducible representations of a reductive group over local or finite fields is naturally partitioned into families according to analytic proper...

Article
ADER Methods for Hyperbolic Equations with a TimeReconstruction Solver for the Generalized Riemann Problem: the Scalar Case
2020欧洲杯体育官方网站 The ADER approach to solve hyperbolic equations to very high order of accuracy has seen explosive developments in the last few years, including both methodological aspects as well as very ambitious application...

Article
Preface to the Focused Issue in Honor of Professor Philip Roe on the Occasion of His 80th Birthday

Article
The Notion of Conservation for Residual Distribution Schemes (or Fluctuation Splitting Schemes), with Some Applications
In this paper, we discuss the notion of discrete conservation for hyperbolic conservation laws. We introduce what we call fluctuation splitting schemes (or residual distribution, also RDS) and show through sev...

Article
Transgressions of the Euler class and Eisenstein cohomology of GL_{N}(Z)
These notes were written to be distributed to the audience of the first author’s Takagi Lectures delivered June 23, 2018. These are based on a workinprogress that is part of a collaborative project that also...

2020欧洲杯体育官方网站 Article
An Approximate Riemann Solver for Advection–Diffusion Based on the Generalized Riemann Problem
2020欧洲杯体育官方网站 We construct an approximate Riemann solver for scalar advection–diffusion equations with piecewise polynomial initial data. The objective is to handle advection and diffusion simultaneously to reduce the inher...

Article
Open AccessSuperconvergence and the Numerical Flux: a Study Using the UpwindBiased Flux in Discontinuous Galerkin Methods
One of the beneficial properties of the discontinuous Galerkin method is the accurate wave propagation properties. That is, the semidiscrete error has dissipation errors of order \(2k+1\)2k+1 (\(\le Ch^{2k+1}\)≤

Article
A ThirdOrder Accurate Wave Propagation Algorithm for Hyperbolic Partial Differential Equations
2020欧洲杯体育官方网站 We extend LeVeque’s wave propagation algorithm, a widely used finite volume method for hyperbolic partial differential equations, to a thirdorder accurate method. The resulting scheme shares main properties w...