Topic
Finite difference method
About: Finite difference method is a research topic. Over the lifetime, 21603 publications have been published within this topic receiving 468852 citations. The topic is also known as: Finite-difference methods & FDM.
Papers published on a yearly basis
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Papers
TL;DR: In this article, a finite difference method is developed to analyze the guided-wave properties of a class of two-dimensional photonic crystals (irregular dielectric rods) for both in-plane and out-of-plane propagation.
Abstract: In this paper, a finite difference method is developed to analyze the guided-wave properties of a class of two-dimensional photonic crystals (irregular dielectric rods). An efficient numerical scheme is developed to deal with the deterministic equations resulting from a set of finite difference equations for inhomogeneous periodic structures. Photonic band structures within an irreducible Brillouin zone are investigated for both in-plane and out-of-plane propagation. For out-of-plane propagation, the guided waves are hybrid modes; while for in-plane propagation, the guided waves are either TE or TM modes, and there exist photonic bandgaps within which wave propagation is prohibited. Photonic bandgap maps for squares, veins, and crosses are investigated to determine the effects of the filling factor, the dielectric contrast, and lattice constants, on the band-gap width and location. Possible applications of photonic bandgap materials are discussed.
135 citations
TL;DR: It appears that the proper finite element equivalents of second-order finite difference schemes are implicit methods of incremental type having third- and fourth-order global accuracy on uniform meshes (Taylor-Galerkin methods).
135 citations
TL;DR: In this article, the authors investigated the achievable accuracy of various time-stepping algorithms and how this can be improved if noise is artificially damped to an acceptable level, and concluded that the Crank-Nicolson scheme with a simple averaging process is superior to the other methods investigated.
Abstract: This paper investigates the phenomenon of ‘noise’ which is common in most time-dependent problems. The emphasis is on the achievable accuracy that is obtained with various time-stepping algorithms and how this can be improved if noise is artificially damped to an acceptable level. A series of experiments are made where the space domain is discretized using the finite element method and the variation with time is approximated by several finite difference methods. The conclusion is reached that the Crank–Nicolson scheme with a simple averaging process is superior to the other methods investigated.
135 citations
TL;DR: This paper investigates an accurate numerical method for solving a biological fractional model via Atangana-Baleanu fractional derivative using the spectral collocation method based on the Chebyshev approximations and presents the effectiveness and accuracy of the proposed method.
Abstract: The main objective of this paper is to investigate an accurate numerical method for solving a biological fractional model via Atangana-Baleanu fractional derivative. We focused our attention on linear and nonlinear Fisher’s equations. We use the spectral collocation method based on the Chebyshev approximations. This method reduced the nonlinear equations to a system of ordinary differential equations by using the properties of Chebyshev polynomials and then solved them by using the finite difference method. This is the first time that this method is used to solve nonlinear equations in Atangana-Baleanu sense. We present the effectiveness and accuracy of the proposed method by computing the absolute error and the residual error functions. The results show that the given procedure is an easy and efficient tool to investigate the solution of nonlinear equations with local and non-local singular kernels.
135 citations
TL;DR: In this article, the Von Neumann stability analysis on the finite-difference equations of a pipe shows that the equations are unconditionally stable and an iterative convergence method is applied to the calculation of node pressure at junctions in networks.
135 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 53 |
| 2024 | 136 |
| 2023 | 170 |
| 2022 | 357 |
| 2021 | 733 |
| 2020 | 690 |