Results 11 to 20 of about 334 (91)
Semidiscrete Vortex Solitons [PDF]
Advanced Photonics Research, 2021 A possibility of creation of stable optical solitons combining one continuous and one discrete coordinates, with embedded vorticity, in an array of planar waveguides with intrinsic cubic–quintic (CQ) nonlinearity is demonstrated. The same system may be realized in terms of the spatiotemporal light propagation in an array of tunnel‐coupled optical ...
Xiaoxi Xu +6 more
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Quenching for discretizations of a semilinear parabolic equation with nonlinear boundary outflux
Journal of Numerical Analysis and Approximation Theory, 2023 In this paper, we study numerical approximations of a semilinear parabolic problem in one-dimension, of which the nonlinearity appears both in source term and in Neumann boundary condition.
Kouakou Cyrille N'Dri +3 more
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Semidiscrete Quantum Droplets and Vortices [PDF]
Physical Review Letters, 2019 We consider a binary bosonic condensate with weak mean-field (MF) residual repulsion, loaded in an array of nearly one-dimensional traps coupled by transverse hopping. With the MF force balanced by the effectively one-dimensional attraction, induced in each trap by the Lee-Hung-Yang correction (produced by quantum fluctuations around the MF state ...
Xiliang Zhang +7 more
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On error-based step size control for discontinuous Galerkin methods for compressible fluid dynamics [PDF]
, 2023 We study temporal step size control of explicit Runge-Kutta methods for compressible computational fluid dynamics (CFD), including the Navier-Stokes equations and hyperbolic systems of conservation laws such as the Euler equations.
Castro, Hugo Guillermo +6 more
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Exponentially accurate Hamiltonian embeddings of symplectic A-stable Runge--Kutta methods for Hamiltonian semilinear evolution equations [PDF]
, 2015 We prove that a class of A-stable symplectic Runge--Kutta time semidiscretizations (including the Gauss--Legendre methods) applied to a class of semilinear Hamiltonian PDEs which are well-posed on spaces of analytic functions with analytic initial data ...
Oliver, Marcel, Wulff, Claudia
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Numerical Awareness in Control [PDF]
, 2004 Algorithm development, sensitivity and accuracy issues, large-scale computations, and high-performance numerical ...
Varga, Andras
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Variational Laplacians for semidiscrete surfaces [PDF]
Advances in Computational Mathematics, 2016 The authors propose a variational definition of the Laplacian on semidiscrete surfaces. Recall that the classical Laplace-Beltrami operator on Riemannian manifolds can be defined via the Dirichlet energy functional with an obvious connection to the mean curvature normal vector.
Carl, Wolfgang, Wallner, Johannes
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ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Volume 103, Issue 11, November 2023., 2023 We consider partitioned time integration for heterogeneous coupled heat equations. First and second order multirate, as well as time‐adaptive Dirichlet‐Neumann Waveform relaxation (DNWR) methods are derived. In 1D and for implicit Euler time integration, we analytically determine optimal relaxation parameters for the fully discrete scheme.
Peter Meisrimel +2 more
wiley +1 more source
Numerical quenching for a semilinear parabolic equation
Mathematical Modelling and Analysis, 2008 This paper concerns the study of the numerical approximation for the nonlinear parabolic boundary value problem with the source term leading to the quenching in finite time.
Diabate Nabongo, Theodore K. Boni
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Sobolev‐orthogonal systems with tridiagonal skew‐Hermitian differentiation matrices
Studies in Applied Mathematics, Volume 150, Issue 2, Page 420-447, February 2023., 2023 Abstract We introduce and develop a theory of orthogonality with respect to Sobolev inner products on the real line for sequences of functions with a tridiagonal, skew‐Hermitian differentiation matrix. While a theory of such L2 ‐orthogonal systems is well established, Sobolev orthogonality requires new concepts and their analysis.
Arieh Iserles, Marcus Webb
wiley +1 more source