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
1 / 2
Papers
TL;DR: A class of finite difference methods for solving fractional diffusion equations is considered, an extension of the weighted average methods for ordinary (non-fractional) diffusion equations, and a simple and accurate stability criterion valid for different discretization schemes of the fractional derivative, arbitrary weight factor, and arbitrary order is found.
333 citations
TL;DR: In this paper, two finite difference/element approaches for the time-fractional subdiffusion equation with Dirichlet boundary conditions are developed, in which the time direction is approximated by the fractional linear multistep method and the space direction by the finite element method.
Abstract: In this paper, two finite difference/element approaches for the time-fractional subdiffusion equation with Dirichlet boundary conditions are developed, in which the time direction is approximated by the fractional linear multistep method and the space direction is approximated by the finite element method. The two methods are unconditionally stable and convergent of order $O(\tau^q+h^{r+1})$ in the $L^2$ norm, where $q=2-\beta$ or 2 when the analytical solution to the subdiffusion equation is sufficiently smooth, $\beta\,(0<\beta<1)$ is the order of the fractional derivative, $\tau$ and $h$ are the step sizes in time and space, respectively, and $r$ is the degree of the polynomial space. The corresponding schemes for the subdiffusion equation with Neumann boundary conditions are presented as well, where the stability and convergence are shown. Numerical examples are provided to verify the theoretical analysis. Comparisons between the algorithms derived in this paper and the existing algorithms are given, ...
330 citations
TL;DR: A simple method for the numerical solution of partial differential equations which embeds the problem within a Cartesian analog of the original equation, posed on the entire space containing the surface.
329 citations
TL;DR: In this article, the authors proposed an orthogonal collocation method for heat and mass transfer with chemical reaction in a catalyst pellet, which is especially suited to situations corresponding to high Thiele modulus when the solution is confined to a thin boundary region near the catalyst surface.
325 citations
TL;DR: In this article, an algorithm for the numerical computation of so-called consistent tangent moduli in finite inelasticity is presented, where the moduli determine the sensitivity of algorithmic expressions for stresses with respect to the change in total deformation.
325 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 53 |
| 2024 | 136 |
| 2023 | 170 |
| 2022 | 357 |
| 2021 | 733 |
| 2020 | 690 |