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Binding properties of sulfur to enable solvent-free fabrication of high-performance polymer-free sulfur-carbon positive electrodes. [PDF]
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On the use of nonstandard finite difference methods†
Journal of Difference Equations and Applications, 2005Many real life problems are modelled by differential equations, for which analytical solutions are not always easy to find. One of the most difficult problems is how to solve these differential equations efficiently. Several researchers have tried to do this in various different ways (e.g. via Finite Element Methods, Standard Finite Difference Methods,
Kailash C Patidar
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Nonstandard finite difference approximation for a generalized Fins problem
Mathematics and Computers in Simulation, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
A. A. Aderogba +4 more
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On the advantages of nonstandard finite differences discretizations for differential problems
Сибирский журнал вычислительной математики, 2022Summary: The goal of this work is to highlight the advantages of using NonStandard Finite Differences (NSFD) numerical schemes for the resolution of Ordinary Differential Equations (ODEs) and Partial Differential Equations (PDEs) of which some properties of the exact solution are a-priori known, such as positivity.
Conte D. +3 more
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Nonstandard finite difference schemes for reaction-diffusion equations
Numerical Methods for Partial Differential Equations, 1999A class of one-dimensional reaction diffusion equations is considered. Assuming polynomial forcing terms, an explicit finite difference scheme with a usual second-order approximation to the diffusion term and a special type of forcing terms discretizations is suggested. The relations between time and space steps are chosen to preserve positivity of the
Ronald E Mickens
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High order nonstandard finite-difference methods
Applied Mathematics and ComputationNonstandard finite difference (NSFD) methods have been considered to overcome some issues of standard methods, particularly when the numerical solution must preserve important properties of the exact solution. These issues increase for high order methods.
Dajana Conte +2 more
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Nonstandard finite difference method by nonlocal approximation
Mathematics and Computers in Simulation, 2003Two types of monotonic properties of solutions of differential equations are discussed and general finite difference schemes, which are stable with respect to these properties are investigated. Apart from being elementary stable, these schemes are also shown to preserve qualitative properties of nonhyperbolic fixed points of the differential equations.
Roumen Anguelov, Jean M.-S. Lubuma
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AN INTRODUCTION TO NONSTANDARD FINITE DIFFERENCE SCHEMES
Journal of Computational Acoustics, 1999Nonstandard finite difference schemes offer the potential for either constructing exact discrete models of differential equations or obtaining discrete models that do not have the elementary numerical instabilities. While the general laws for constructing such schemes are not precisely known at the present time, a number of important rules have been ...
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Divergence Properties of the Nonstandard Finite Difference Methods
IEEE Microwave and Wireless Components Letters, 2007Yee's classic algorithm was proved to be divergence-free in source-free regions. However, the divergence properties of the nonstandard finite difference (NSFD) methods have not been addressed. In this letter, we investigate the divergence nature of the NSFD (2,2) and (2,4) algorithms.
Bo Yang, Constantine A. Balanis
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