Positivity Preserving Interpolation Using Rational Bicubic Spline [PDF]
Journal of Applied Mathematics, 2015 This paper discusses the positivity preserving interpolation for positive surfaces data by extending the C1 rational cubic spline interpolant of Karim and Kong to the bivariate cases. The partially blended rational bicubic spline has 12 parameters in the
Samsul Ariffin Abdul Karim +2 more
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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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Positivity-Preserving Analysis of Numerical Schemes for Ideal Magnetohydrodynamics [PDF]
SIAM Journal on Numerical Analysis, 2018 Accepted for publication in SIAM Journal on Numerical ...
Kailiang Wu
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Positivity-preserving adaptive Runge–Kutta methods [PDF]
Communications in Applied Mathematics and Computational Science, 2021 Many important differential equations model quantities whose value must remain positive or stay in some bounded interval. These bounds may not be preserved when the model is solved numerically. We propose to ensure positivity or other bounds by applying Runge-Kutta integration in which the method weights are adapted in order to enforce the bounds.
Stephan Nüßlein +2 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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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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Positivity-preserving methods for population models
CoRR, 2021 Many important applications are modelled by differential equations with positive solutions. However, it remains an outstanding open problem to develop numerical methods that are both (i) of a high order of accuracy and (ii) capable of preserving positivity.
Sergio Blanes +2 more
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