Results 1 to 10 of about 331,423 (159)
A split-step finite element method for the space-fractional Schrödinger equation in two dimensions [PDF]
Scientific ReportsIn this article, we propose a split-step finite element method (FEM) for the two-dimensional nonlinear Schrödinger equation (NLS) with Riesz fractional derivatives in space. The space-fractional NLS is first spatially discretized by finite element scheme
Xiaogang Zhu, Haiyang Wan, Yaping Zhang
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A semi-discrete large-time behavior preserving scheme for the augmented Burgers equation [PDF]
ESAIM: Mathematical Modelling and Numerical Analysis, 2017 In this paper we analyze the large-time behavior of the augmented Burgers equation. We first study the well-posedness of the Cauchy problem and obtain $L^1$-$L^p$ decay rates.
Ignat, Liviu I., Pozo, Alejandro
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An energy stable discontinuous Galerkin time-domain finite element method in optics and photonics
Results in Applied Mathematics, 2023 In this paper, a time-domain discontinuous Galerkin (TDdG) finite element method for the full system of Maxwell’s equations in optics and photonics is investigated, including a complete proof of a semi-discrete error estimate.
Asad Anees, Lutz Angermann
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A semi-discrete numerical scheme for nonlocally regularized KdV-type equations [PDF]
Applied Numerical Mathematics, 2022 A general class of KdV-type wave equations regularized with a convolution-type nonlocality in space is considered. The class differs from the class of the nonlinear nonlocal unidirectional wave equations previously studied by the addition of a linear convolution term involving third-order derivative.
H.A. Erbay, S. Erbay, A. Erkip
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A New Entropy Stable Finite Difference Scheme for Hyperbolic Systems of Conservation Laws
Mathematics, 2023 The hyperbolic problem has a unique entropy solution, which maintains the entropy inequality. As such, people hope that the numerical results should maintain the discrete entropy inequalities accordingly. In view of this, people tend to construct entropy
Zhizhuang Zhang +4 more
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Entropy Dissipation Semi-Discretization Schemes for Fokker–Planck Equations [PDF]
Journal of Dynamics and Differential Equations, 2018 We propose a new semi-discretization scheme to approximate nonlinear Fokker-Planck equations, by exploiting the gradient flow structures with respect to the 2-Wasserstein metric. We discretize the underlying state by a finite graph and define a discrete 2-Wasserstein metric.
Shui-Nee Chow +3 more
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AIMS Mathematics, 2023 The paper considers the Hamiltonian structure and develops efficient energy-preserving schemes for the nonlinear wave equation with a fractional Laplacian operator. To this end, we first derive the Hamiltonian form of the equation by using the fractional
Tingting Ma , Yuehua He
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A semi-discrete scheme for the stochastic Landau–Lifshitz equation [PDF]
Stochastic Partial Differential Equations: Analysis and Computations, 2014 We propose a new convergent time semi-discrete scheme for the stochastic Landau-Lifshitz-Gilbert equation. The scheme is only linearly implicit and does not require the resolution of a nonlinear problem at each time step. Using a martingale approach, we prove the convergence in law of the scheme up to a subsequence.
Alouges, François +2 more
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Entropy-dissipating semi-discrete Runge-Kutta schemes for nonlinear diffusion equations [PDF]
Communications in Mathematical Sciences, 2015 Semi-discrete Runge-Kutta schemes for nonlinear diffusion equations of parabolic type are analyzed. Conditions are determined under which the schemes dissipate the discrete entropy locally. The dissipation property is a consequence of the concavity of the difference of the entropies at two consecutive time steps.
Jüngel, Ansgar, Schuchnigg, Stefan
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A high-order convergence analysis for semi-Lagrangian scheme of the Burgers' equation
AIMS Mathematics, 2023 In this article, we provide a comprehensive convergence and stability analysis of a semi-Lagrangian scheme for solving nonlinear Burgers' equations with a high-order spatial discretization.
Philsu Kim , Seongook Heo, Dojin Kim
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