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: This paper presents dissipation operators that preserve both stability and accuracy for high order finite difference approximations of initial boundary value problems.
Abstract: Stability for nonlinear convection problems using centered difference schemes require the addition of artificial dissipation. In this paper we present dissipation operators that preserve both stability and accuracy for high order finite difference approximations of initial boundary value problems.
205 citations
TL;DR: In this paper, a finite difference method for the numerical solution of partial integro-differential equations is considered and the convergence order in time is shown to be greater than one, which is confirmed by a numerical example.
204 citations
TL;DR: In this paper, the authors describe a fourth-order finite difference model of the equatorial ocean that is designed to study dynamic and thermodynamic processes on time scales of a decade or less.
204 citations
TL;DR: Finite difference methods for the Gross-Pitaevskii equation with an angular momentum rotation term in two and three dimensions are analyzed and error bounds on the errors between the mass and energy in the discretized level and their corresponding continuous counterparts are derived.
Abstract: We analyze finite difference methods for the Gross-Pitaevskii equation with an angular momentum rotation term in two and three dimensions and obtain the optimal convergence rate, for the conservative Crank-Nicolson finite difference (CNFD) method and semi-implicit finite difference (SIFD) method, at the order of O(h2 + τ2) in the l2-norm and discrete H1-norm with time step τ and mesh size h. Besides the standard techniques of the energy method, the key technique in the analysis for the SIFD method is to use the mathematical induction, and resp., for the CNFD method is to obtain a priori bound of the numerical solution in the l∞-norm by using the inverse inequality and the l2-norm error estimate. In addition, for the SIFD method, we also derive error bounds on the errors between the mass and energy in the discretized level and their corresponding continuous counterparts, respectively, which are at the same order of the convergence rate as that of the numerical solution itself. Finally, numerical results are reported to confirm our error estimates of the numerical methods.
203 citations
TL;DR: A new unified methodology to derive spatial finite-difference coefficients in the joint time-space domain to reduce numerical dispersion and can be easily extended to solve similar partial difference equations arising in other fields of science and engineering.
203 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 53 |
| 2024 | 136 |
| 2023 | 170 |
| 2022 | 357 |
| 2021 | 733 |
| 2020 | 690 |