Results 181 to 190 of about 252,020 (241)
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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 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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Nonstandard Finite Difference Scheme for the Epidemic Model with Vaccination
Journal of Mathematical ScienceszbMATH Open Web Interface contents unavailable due to conflicting licenses.
Badarch Tumurkhuyag, Balt Batgerel
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A new positivity-preserving nonstandard finite difference scheme for the DWE
Numerical Methods for Partial Differential Equations, 2005AbstractAn improved positivity‐preserving nonstandard finite difference scheme for the linear damped wave equation is presented. Unlike an earlier such scheme developed by the authors, the new scheme involves three time levels and is therefore able to include the effects of the equation's relaxation coefficient. © 2005 Wiley Periodicals, Inc.
Ronald E Mickens, P M Jordan
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Nonstandard Finite Difference Theta Approaches to the Predator–Prey System
Mathematical Methods in the Applied SciencesIn this paper, we propose nonstandard finite difference theta schemes for a well‐known Lotka‐Volterra model without the Allee effect and investigate the dynamical behavior of the discretized system.
Nihal Özdoğan, Bahar Arslan
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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 general two-dimensional autonomous dynamical systems
Applied Mathematics Letters, 2005 General two-dimensional autonomous dynamical systems and their standard numerical discretizations are considered. Nonstandard stability-preserving finite-difference schemes based on the explicit and implicit Euler and the second-order Runge–Kutta methods
Hristo V Kojouharov
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Mathematical methods in the applied sciences, 2022
A newly disclosed nonstandard finite difference method has been used to discretize a Lotka–Volterra model to investigate the critical normal form coefficients of bifurcations for both one‐parameter and two‐parameter bifurcations.
Z. Eskandari +3 more
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A newly disclosed nonstandard finite difference method has been used to discretize a Lotka–Volterra model to investigate the critical normal form coefficients of bifurcations for both one‐parameter and two‐parameter bifurcations.
Z. Eskandari +3 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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International Journal of Computational Mathematics, 2023
In this paper, we extend the Mickens' methodology to construct a second-order nonstandard finite difference (NSFD) method, which preserves dynamical properties including positivity, local asymptotic stability and especially, global asymptotic stability ...
M. T. Hoang
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In this paper, we extend the Mickens' methodology to construct a second-order nonstandard finite difference (NSFD) method, which preserves dynamical properties including positivity, local asymptotic stability and especially, global asymptotic stability ...
M. T. Hoang
semanticscholar +1 more source