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Showing 1 to 6 of 6 for “"Riemann-Hilbert problems"”.
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A Riemann-Hilbert approach to scattering on a one-dimensional semi-infinite crystal
… crystal is analyzed using the method of the Riemann-Hilbert Problem for analytic functions. We proceed in the framework of the limiting absorption principle. Our formulas allow to find the scattered field at any point of the crystal. In particular, we obtain an explicit formula for the …
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Analytic Solutions for Flows Through Cascades
… in the form of singular integral equations, Riemann--Hilbert problems, the Wiener--Hopf method and conformal mappings via the transcendental Schottky--Klein prime function. These methods are applied in the context of rigorous asymptotic expansions where the solution is expanded in terms of a …
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A Riemann-Hilbert Approach to the Kissing Polynomials
… known as the Kissing Polynomials through Riemann-Hilbert techniques. The Kissing Polynomials are a family of non-Hermitian orthogonal polynomials, which are orthogonal with respect to the complex weight function $\exp(i\omega z)$ over the interval $[-1,1]$, where $\omega>0$. Although they …
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Exact Solutions to the Six-Vertex Model with Domain Wall Boundary Conditions and Uniform Asymptotics of Discrete Orthogonal Polynomials on an Infinite Lattice
… develop an asymptotic analysis, based on a Riemann-Hilbert approach, for orthogonal polynomials on an infinite regular lattice with respect to varying exponential weights. The general method and results of this analysis are given in Chapter 5 of this dissertation.
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Solution of fully-coupled shallow water equations and contaminant transport using a primitive variable Riemann solver and a semi-discrete SUPG method
… bed topography and wetting-drying fronts. A Riemann-solver finite volume scheme, using primitive variables rather than conserved variables, and a semi-discrete Streamline Upwind Petrov-Galerkin (SUPG) method in finite element context are applied to compare the performance of these two …