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: The asymptotic stability and the absolute stability of these methods are proved and error representations and estimates for the truncation, propagation and global error are derived.
Abstract: This paper is devoted to the numerical treatment of fractional differential equations. Based on the Grunwald-Letnikov definition of fractional derivatives, finite difference schemes for the approximation of the solution are discussed. The main properties of these explicit and implicit methods concerning the stability, the convergence and the error behavior are studied related to linear test equations. The asymptotic stability and the absolute stability of these methods are proved. Error representations and estimates for the truncation, propagation and global error are derived. Numerical experiments are given.
397 citations
TL;DR: In this paper, a front-tracking method is presented to simulate time dependent two-dimensional dendritic solidification of pure substances, based on a finite difference approximation of the heat equation and explicit tracking of the liquid?solid interface.
394 citations
TL;DR: In this paper, a multivariate interpolation scheme for coupling fluid and structural models in 3D space is presented using radial basis functions for numerical aeroelastic computations, a selection of applicable functions is chosen: a classical without compact support, and some recently presented smooth compactly supported radial basis function.
386 citations
TL;DR: An anomalous subdiffusion equation (ASub-DE) is considered and a new implicit numerical method (INM) and two solution techniques for improving the order of convergence of the INM for solving the ASub-DE are proposed.
Abstract: A physical-mathematical approach to anomalous diffusion is based on a generalized diffusion equation containing derivatives of fractional order. In this paper, an anomalous subdiffusion equation (ASub-DE) is considered. A new implicit numerical method (INM) and two solution techniques for improving the order of convergence of the INM for solving the ASub-DE are proposed. The stability and convergence of the INM are investigated by the energy method. Some numerical examples are given. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and supporting theoretical results can also be applied to other fractional integro-differential equations and higher-dimensional problems.
385 citations
TL;DR: In this article, a numerical method to simulate liquid-vapor phase change is presented, based on the so-called single field formulation where one set of equations for conservation of mass, momentum and energy are written for the entire flow field.
383 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 53 |
| 2024 | 136 |
| 2023 | 170 |
| 2022 | 357 |
| 2021 | 733 |
| 2020 | 690 |