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: A bird’s eye view on the development of numerical methods for solving partial differential equations with a particular emphasis on nonlinear PDEs is provided.
Abstract: Numerical methods were first put into use as an effective tool for solving partial differential equations (PDEs) by John von Neumann in the mid1940s. In a 1949 letter von Neumann wrote “the entire computing machine is merely one component of a greater whole, namely, of the unity formed by the computing machine, the mathematical problems that go with it, and the type of planning which is called by both.” The “greater whole” is viewed today as scientific computation: over the past sixty years, scientific computation has emerged as the most versatile tool to complement theory and experiments, and numerical methods for solving PDEs are at the heart of many of today’s advanced scientific computations. Numerical solutions found their way from financial models on Wall Street to traffic models on Main Street. Here we provide a bird’s eye view on the development of these numerical methods with a particular emphasis on nonlinear PDEs.
216 citations
TL;DR: In this article, the analytical partial derivatives of the plane wave EXAFS function can be calcalated using cubic spline, which decreases the CPU time needed for a refinement by over 60% for a three shell system compared to a refinement with partial derivaties calculated with the finite difference method.
Abstract: Parameterization of phase and backscattering amplitude with cubic splines is described. Using the cubic spline, the analytical partial derivatives of the plane wave EXAFS function can be calcalated. The use of analytical partial derivatives decreases the CPU time needed for a refinement by over 60% for a three shell system compared to a refinement with partial derivaties calculated with the finite difference method.
216 citations
TL;DR: In this article, the Sunde logarithmic approximation for the single-wire line ground impedance was extended to the case of a multiconductor line, where the inverse Fourier transform of the ground impedance presents singularities which complicate the numerical solution of the transmission line equations.
Abstract: In this paper, we first extend the Sunde logarithmic approximation for the single-wire line ground impedance to the case of a multiconductor line. The new approximate forms are compared to the general expressions which involve integrals over an infinitely long interval and an excellent agreement is found. The inverse Fourier transform of the ground impedance presents singularities which complicate the numerical solution of the transmission line equations. The order of the singularity is reduced by 1, and a careful numerical treatment is then employed to derive an equivalent and numerically more appropriate form of coupling equations in which there is no longer a singular term. Finally, finite-difference time-domain (FDTD) solutions of the coupling equations are presented and the theory is applied to calculate lightning-induced voltages on a multiconductor line. The lightning-induced voltages are calculated for the case of lossless/lossy, single-conductor/multiconductor lines and the effect of ground losses and the presence of other conductors on the magnitude and shape of induced voltages are illustrated.
215 citations
TL;DR: A brief survey of numerical methods for time-dependent advection-dominated partial differential equations (PDEs) is given in this paper, including first-order hyperbolic PDEs and non-stationary ADVDEs.
215 citations
TL;DR: Systematic numerical experiments indicate that a second order implicit time discretization of the viscous term, with the pressure and convective terms treated explicitly, is stable under the standard CFL condition.
215 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 53 |
| 2024 | 136 |
| 2023 | 170 |
| 2022 | 357 |
| 2021 | 733 |
| 2020 | 690 |