Results 31 to 40 of about 7,957,612 (305)
Issues with positivity-preserving Patankar-type schemes [PDF]
Applied Numerical Mathematics, 2021 Patankar-type schemes are linearly implicit time integration methods designed to be unconditionally positivity-preserving. However, there are only little results on their stability or robustness.
Davide Torlo +2 more
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Positivity-preserving well-balanced central discontinuous Galerkin schemes for the Euler equations under gravitational fields [PDF]
Journal of Computational Physics, 2022 This paper designs and analyzes positivity-preserving well-balanced (WB) central discontinuous Galerkin (CDG) schemes for the Euler equations with gravity. A distinctive feature of these schemes is that they not only are WB for a general known stationary
Haili Jiang, Huazhong Tang, Kailiang Wu
semanticscholar +1 more source
Positivity-preserving methods for ordinary differential equations [PDF]
ESAIM: Mathematical Modelling and Numerical Analysis, 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 ...
S. Blanes, A. Iserles, S. MacNamara
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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
openaire +2 more sources
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
openaire +4 more sources
Numerical solution of a malignant invasion model using some finite difference methods
Demonstratio Mathematica, 2023 In this article, one standard and four nonstandard finite difference methods are used to solve a cross-diffusion malignant invasion model. The model consists of a system of nonlinear coupled partial differential equations (PDEs) subject to specified ...
Appadu Appanah Rao +1 more
doaj +1 more source
Monotonicity-preserving splitting schemes for solving balance laws [PDF]
Iranian Journal of Numerical Analysis and Optimization, 2021 In this paper, some monotonicity-preserving (MP) and positivity-preserving (PP) splitting methods for solving the balance laws of the reaction and diffusion source terms are investigated.
F. Khodadosti, J. Farzi, M.M. Khalsaraei
doaj +1 more source
High order positivity-preserving numerical methods for a non-local photochemical model [PDF]
ESAIM: Mathematical Modelling and Numerical AnalysisIn this paper we design high-order positivity-preserving approximation schemes for an integro-differential model describing photochemical reactions. Specifically, we introduce and analyze three classes of dynamically consistent methods, encompassing non ...
Mario Pezzella
semanticscholar +1 more source
Nonlinear dynamics, 2021 We propose a positivity-preserving finite volume scheme on non-conforming quadrilateral distorted meshes with hanging nodes for subdiffusion equations, where the differential equations have a sum of time-fractional derivatives of different orders, and ...
Xuehua Yang +3 more
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An Arbitrary High Order and Positivity Preserving Method for the Shallow Water Equations [PDF]
Computers & Fluids, 2021 In this paper, we develop and present an arbitrary high order well-balanced finite volume WENO method combined with the modified Patankar Deferred Correction (mPDeC) time integration method for the shallow water equations.
M. Ciallella +3 more
semanticscholar +1 more source