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.
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TL;DR: Most of the theoretical results hold for the related Swift-Hohenberg equation as well and local-in-time error estimates that ensure the convergence of the scheme are presented.
Abstract: We present an unconditionally energy stable finite-difference scheme for the phase field crystal equation. The method is based on a convex splitting of a discrete energy and is semi-implicit. The equation at the implicit time level is nonlinear but represents the gradient of a strictly convex function and is thus uniquely solvable, regardless of time step size. We present local-in-time error estimates that ensure the convergence of the scheme. While this paper is primarily concerned with the phase field crystal equation, most of the theoretical results hold for the related Swift-Hohenberg equation as well.
402 citations
TL;DR: In this paper, the alternating direction implicit (ADI) technique is applied in formulating the finite-difference time-domain (FDTD) algorithm, which is free of the constraint of the Courant stability condition.
Abstract: In this paper, a finite-difference time-domain method that is free of the constraint of the Courant stability condition is presented for solving electromagnetic problems. In it, the alternating direction implicit (ADI) technique is applied in formulating the finite-difference time-domain (FDTD) algorithm. Although the resulting formulations are computationally more complicated than the conventional FDTD, the proposed FDTD is very appealing since the time step used in the simulation is no longer restricted by stability but by accuracy. As a result, computation speed can be improved. It is found that the number of iterations with the proposed FDTD can be at least three times less than that with the conventional FDTD with the same numerical accuracy.
401 citations
TL;DR: Several finite difference schemes are discussed for solving the two-dimensional Schrodinger equation with Dirichlet's boundary conditions with the unique advantage of the Barakat and Clark technique, which is unconditionally stable and is explicit in nature.
400 citations
TL;DR: The comparison with the corresponding results of finite difference methods by the L1 formula demonstrates that the new L1-2 formula is much more effective and more accurate than the L2 formula when solving time-fractional differential equations numerically.
400 citations
Book•
01 May 1982
TL;DR: An overview of the fundamental concepts and applications of computerized groundwater modeling can be found in this paper, where the authors present an overview of some of the basic concepts and application of groundwater modeling.
Abstract: Introduction to Groundwater Modeling presents an overview of the fundamental concepts and applications of computerized groundwater modeling.
399 citations