A Positivity-Preserving Finite Volume Scheme for Nonequilibrium Radiation Diffusion Equations on Distorted Meshes [PDF]
Entropy, 2022 In this paper, we propose a new positivity-preserving finite volume scheme with fixed stencils for the nonequilibrium radiation diffusion equations on distorted meshes.
Di Yang, Gang Peng, Zhiming Gao
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Positivity-Preserving Hybridizable Discontinuous Galerkin Scheme for Solving PNP Model [PDF]
EntropyWe introduce a hybridizable discontinuous Galerkin (HDG) scheme for solving the Poisson–Nernst–Planck (PNP) equations. The log-density formulation as introduced by Metti et al. in their paper “Energetically stable discretizations for charge transport and
Diana Morales, Zhiliang Xu
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Stability analysis and numerical simulation of nonlocal extended epidemic models using positivity-preserving scheme [PDF]
Scientific ReportsIn this paper we introduce a robust numerical framework for simulating the nonlocal extended epidemic models that incorporate the fractional diffusion to capture the complex spatial–temporal dynamics of disease spread. The presented numerical scheme uses
Muhammad Yousuf, Narjes Alshakhoury
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THE SLICE BALANCE APPROACH USING AN ADAPTIVE-WEIGHTED CLOSURE [PDF]
EPJ Web of Conferences, 2021 In this paper, we present a formulation of the slice balance approach using a nonlinear closure relation derived analogously from the adaptive-weighted diamond-difference form of the weighted diamond-difference method for Cartesian grids.
Hackemack Michael W.
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Preserving Positive Intermediate Curvature
The Journal of Geometric Analysis, 2023 AbstractConsider a compact manifoldN(with or without boundary) of dimensionn. Positivem-intermediate curvature interpolates between positive Ricci curvature ($$m = 1$$m=1) and positive scalar curvature ($$m = n-1$$m=n-1), and it is obstructed on partial tori$$N^n = M^{n-m} \times \mathbb {T}^m$$Nn=Mn-m×Tm. Given Riemannian metrics$$g, {\bar{g}}$$g,g¯on$
Tsz-Kiu Aaron Chow +2 more
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Qualitatively Stable Schemes for the Black–Scholes Equation
Fractal and Fractional, 2023 In this paper, the Black–Scholes equation is solved using a new technique. This scheme is derived by combining the Laplace transform method and the nonstandard finite difference (NSFD) strategy. The qualitative properties of the method are discussed, and
Mohammad Mehdizadeh Khalsaraei +5 more
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Experiments with a Positivity-Preserving Operator [PDF]
Experimental Mathematics, 2008 We consider some multivariate rational functions which have (or are conjectured to have) only positive coefficients in their series expansion. We consider an operator that preserves positivity of series coefficients, and apply the inverse of this operator to the rational functions.
Manuel Kauers, Doron Zeilberger
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Positivity preserving results for a biharmonic equation under Dirichlet boundary conditions [PDF]
Opuscula Mathematica, 2014 We prove a dichotomy result giving the positivity preserving property for a biharmonic equation with Dirichlet boundary conditions arising in MEMS models. We adapt some ideas in [H.-Ch. Grunau, G.
Hanen Ben Omrane, Saïma Khenissy
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Some standard and nonstandard finite difference schemes for a reaction–diffusion–chemotaxis model
Open Physics, 2023 Two standard and two nonstandard finite difference schemes are constructed to solve a basic reaction–diffusion–chemotaxis model, for which no exact solution is known.
de Waal Gysbert Nicolaas +2 more
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An Unconditional Positivity-Preserving Difference Scheme for Models of Cancer Migration and Invasion
Mathematics, 2022 In this paper, we consider models of cancer migration and invasion, which consist of two nonlinear parabolic equations (one of the convection–diffusion reaction type and the other of the diffusion–reaction type) and an additional nonlinear ordinary ...
Mikhail K. Kolev +2 more
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