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
Papers
More filters
TL;DR: In this paper, a model for studying ocean circulation problems taking into account the complicated outline and bottom topography of the World Ocean is presented, and the model is designed to be as consistent as possible with the continuous equations with respect to energy.
1,048 citations
TL;DR: Finite element and finite difference methods are combined with the method of characteristics to treat a parabolic problem of the form $cu_t + bu_x - (au_x )_x = f as mentioned in this paper.
Abstract: Finite element and finite difference methods are combined with the method of characteristics to treat a parabolic problem of the form $cu_t + bu_x - (au_x )_x = f$. Optimal order error estimates in $L^2 $ and $W^{1,2} $ are derived for the finite element procedure. Various error estimates are presented for a variety of finite difference methods. The estimates show that, for convection-dominated problems $(b \gg a)$, these schemes have much smaller time-truncation errors than those of standard methods. Extensions to n-space variables and time-dependent or nonlinear coefficients are indicated, along with applications of the concepts to certain problems described by systems of differential equations.
1,018 citations
Book•
01 Feb 1980
TL;DR: The authors created Reference Record created on 2005-11-18, modified on 2016-08-08, and used it to build a reference record for mathematical calculiques and differentielles.
Abstract: Keywords: elements : finis ; equations : differentielles ; methodes de : calcul ; mathematiques Reference Record created on 2005-11-18, modified on 2016-08-08
1,003 citations
TL;DR: This work systematically analyze the performance of implicit-explicit IMEX schemes, propose improved new schemes, and pay particular attention to their relative performance in the context of fast multigrid algorithms and of aliasing reduction for spectral methods.
Abstract: Implicit-explicit (IMEX) schemes have been widely used, especially in conjunction with spectral methods, for the time integration of spatially discretized partial differential equations (PDEs) of diffusion-convection type. Typically, an implicit scheme is used for the diffusion term and an explicit scheme is used for the convection term. Reaction-diffusion problems can also be approximated in this manner. In this work we systematically analyze the performance of such schemes, propose improved new schemes, and pay particular attention to their relative performance in the context of fast multigrid algorithms and of aliasing reduction for spectral methods.For the prototype linear advection-diffusion equation, a stability analysis for first-, second-, third-, and fourth-order multistep IMEX schemes is performed. Stable schemes permitting large time steps for a wide variety of problems and yielding appropriate decay of high frequency error modes are identified. Numerical experiments demonstrate that weak decay...
963 citations
Book•
04 Nov 2019
TL;DR: In this paper, the authors consider linear initial value problems, Sturm-Liouville problems and related inequalities in several independent variables, including difference inequalities and boundary value problems for linear systems and nonlinear systems.
Abstract: Preliminaries linear initial value problems miscellaneous difference equations difference inequalities qualitative properties of solutions of difference systems qualitative properties of solutions of higher order difference equations qualitative properties of solutions of neutral difference equations boundary value problems for linear systems boundary value problems for nonlinear systems miscellaneous properties of solutions of higher order linear difference equations boundary value problems for higher order difference equations Sturm-Liouville problems and related inequalities difference inequalities in several independent variables.
939 citations