Nonstandard finite difference method by nonlocal approximation

Anguelov, Roumen; Lubuma, Jean M.‐S.

doi:10.1016/s0378-4754(02)00106-4

Cited by 126 publications

(123 citation statements)

References 6 publications

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“…This formulation is well known as the nonstandard finite-difference time-domain method NS-FDTD [16,21,34]. The main rules to construct a nonstandard scheme are [16]:…”

Section: From the Flexible Fdtd Scheme Of The Element-oriented Model mentioning

confidence: 99%

A New Element-Oriented Model for Computational Electromagnetics

Ziyyat¹

2012

PIER B

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Abstract-In this paper, we present a new model using a Fourdimensional (4D) Element-Oriented physical concepts based on a topological approach in electromagnetism.Its general finite formulation on dual staggered grids reveals a flexible Finite-Difference Time-Domain (FDTD) method with reasonable local approximating functions. This flexible FDTD method is developed without recourse to the traditional Taylor based forms of the individual differential operators. This new formulation generalizes both the standard FDTD (S-FDTD) and the nonstandard FDTD (NS-FDTD) methods. Moreover, it can be used to generate new numerical methods. As proof, we deduce a new nonstandard scheme more accurate than the S-FDTD and the known nonstandard NS-FDTD methods. Through some numerical examples, we validate this proposal, and we show the power and the advantage of this Element-Oriented Model.

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“…This formulation is well known as the nonstandard finite-difference time-domain method NS-FDTD [16,21,34]. The main rules to construct a nonstandard scheme are [16]:…”

Section: From the Flexible Fdtd Scheme Of The Element-oriented Model mentioning

confidence: 99%

A New Element-Oriented Model for Computational Electromagnetics

Ziyyat¹

2012

PIER B

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“…Note that 2 is the rate of successful treatment of , ∈ { , , } equations (PDEs) with more accuracy than standard finite difference method (SFDM). It is considered as a powerful numerical scheme that preserves properties of exact solutions of the differential equation [36]. The main aim of work is to study numerically the solutions of fractional-order model of multistrain TB with time delay memory.…”

Section: Introductionmentioning

confidence: 99%

Numerical Study for Time Delay Multistrain Tuberculosis Model of Fractional Order

2017

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A novel mathematical fractional model of multistrain tuberculosis with time delay memory is presented. The proposed model is governed by a system of fractional delay differential equations, where the fractional derivative is defined in the sense of the Grünwald-Letinkov definition. Modified parameters are introduced to account for the fractional order. The stability of the equilibrium points is investigated for any time delay. Nonstandard finite deference method is proposed to solve the resulting system of fractional-order delay differential equations. Numerical simulations show that nonstandard finite difference method can be applied to solve such fractional delay differential equations simply and effectively.

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“…But, time step freedom is provided by the non-standard finite difference method that is mentioned in the paper. Interest of the paper is to improve the non-standard finite different method that showed in [1]. R. Anguelov and J.M.-S. Lubuma interest is non-linear terms of ODEs.…”

Section: Introductionmentioning

confidence: 99%

“…Here, T could be ∞ but t 0 is finite. As in shown in [1], numerical approximation of (1) is replace the continuous interval [t 0 , T ) by the mesh of discrete points…”

Section: Introductionmentioning

confidence: 99%

Nonstandard finite difference method for ODEs for initial-value problems

Celik¹

2016

ntmsci

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Abstract:In this paper, a powerful recent non-standard finite different method by nonlocal approximation is improved. Also, compared standard finite difference method to this non-standard finite different method in terms of stability and accuracy. As a numerical example, Hybrid Selection & Genetics equation is considered as the candidate from class of first order ODEs with polynomial right-hand sides. Furthermore, results obtained from the non-standard finite different method and MATLAB ODE solvers (ode15s,ode23s) compared in terms of stability, accuracy, and execution time.

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Nonstandard finite difference method by nonlocal approximation

Cited by 126 publications

References 6 publications

A New Element-Oriented Model for Computational Electromagnetics

A New Element-Oriented Model for Computational Electromagnetics

Numerical Study for Time Delay Multistrain Tuberculosis Model of Fractional Order

Nonstandard finite difference method for ODEs for initial-value problems

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