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    Book

  2. Book Series

    Applied Mathematical Sciences

    2020欧洲杯体育官方网站Volume 1 / 1971 to Volume 203 / 2021

  3. No Access2020欧洲杯体育官方网站

    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 self-adjoint boundary condition. We show ho...

    Tuncay Aktosun, Ricardo Weder in Direct and Inverse Scattering for the Matr… (2021)

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    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...

    Tuncay Aktosun, Ricardo Weder in Direct and Inverse Scattering for the Matr… (2021)

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    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...

    Tuncay Aktosun, Ricardo Weder in Direct and Inverse Scattering for the Matr… (2021)

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    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...

    Tuncay Aktosun, Ricardo Weder in Direct and Inverse Scattering for the Matr… (2021)

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    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 half-line matrix Schrödinger equation using an input data set consisting of a matrix potential and a self-adjoint boundary condi...

    Tuncay Aktosun, Ricardo Weder in Direct and Inverse Scattering for the Matr… (2021)

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    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...

    Tuncay Aktosun, Ricardo Weder in Direct and Inverse Scattering for the Matr… (2021)

  9. Journal

    Japanese Journal of Mathematics

    Volume 1 / 2006 - Volume 15 / 2020

  10. 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

  11. 2020欧洲杯体育官方网站 Article

    Open Access

    A Multi-physics 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 ...

    Louisa Michael, Stephen T. Millmore in Communications on Applied Mathematics and … (2020)

  12. Article

    My Way: A Computational Autobiography

    2020欧洲杯体育官方网站 In this paper, the author recounts his forty-year plus struggle to find a sound basis for understanding the computational fluid dynamics of compressible flow.

    Philip Roe in Communications on Applied Mathematics and Computation (2020)

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    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...

    Shamgar Gurevich, Roger Howe in Japanese Journal of Mathematics (2020)

  14. Article

    ADER Methods for Hyperbolic Equations with a Time-Reconstruction 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...

    R. Demattè, V. A. Titarev, G. I. Montecinos in Communications on Applied Mathematics and … (2020)

  15. Article

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

    Rémi Abgrall, Jennifer K. Ryan, Chi-Wang Shu in Communications on Applied Mathematics and … (2020)

  16. 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...

    Rémi Abgrall in Communications on Applied Mathematics and Computation (2020)

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    Article

    Transgressions of the Euler class and Eisenstein cohomology of GLN(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 work-in-progress that is part of a collaborative project that also...

    Nicolas Bergeron, Pierre Charollois, Luis E. Garcia in Japanese Journal of Mathematics (2020)

  18. 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...

    Steven Jöns, Claus-Dieter Munz in Communications on Applied Mathematics and Computation (2020)

  19. Article

    Open Access

    Superconvergence and the Numerical Flux: a Study Using the Upwind-Biased Flux in Discontinuous Galerkin Methods

    One of the beneficial properties of the discontinuous Galerkin method is the accurate wave propagation properties. That is, the semi-discrete error has dissipation errors of order \(2k+1\)2k+1 (\(\le Ch^{2k+1}\)

    Daniel J. Frean, Jennifer K. Ryan in Communications on Applied Mathematics and Computation (2020)

  20. Article

    A Third-Order 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 third-order accurate method. The resulting scheme shares main properties w...

    Christiane Helzel in Communications on Applied Mathematics and Computation (2020)

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