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: In this article, a finite difference solution of the transient free-convection flow of an incompressible viscous fluid past an impulsively started semi-infinite vertical plate with heat and mass transfer is presented.
Abstract: Finite difference solution of the transient free-convection flow of an incompressible viscous fluid past an impulsively started semi-infinite vertical plate with heat and mass transfer is presented here. The steady state velocity, temperature and concentration profiles are shown graphically. Velocity profiles are compared with exact solution. It has been observed that there is a rise in the velocity due to the presence of a mass diffusion. An increase in Schmidt number, leads to a fall in the velocity. Stability and the convergence of the finite difference scheme are established.
76 citations
TL;DR: In this article, the finite difference method due to Lax (1954) is used to solve the equations of motion for a cylindrically symmetric flow of a compressible fluid.
Abstract: The finite difference method due to Lax (1954) is used to solve the equations of motion for a cylindrically symmetric flow of a compressible fluid. In particular, a converging cylindrical shock is found to increase in strength in agreement with the formula of Chisnell (1957). The artificial diffusion introduced by the method causes the pressure to remain finite at the axis, but a reflected diverging shock is obtained.
76 citations
TL;DR: Nonstandard stability-preserving finite-difference schemes based on the explicit and implicit Euler and the second-order Runge–Kutta methods are designed and analyzed.
76 citations
TL;DR: In this article, the complex natural frequencies for linear free vibrations and bifurcation and chaos for forced nonlinear vibration of axially moving viscoelastic plate are investigated.
Abstract: The complex natural frequencies for linear free vibrations and bifurcation and chaos for forced nonlinear vibration of axially moving viscoelastic plate are investigated in this paper. The governing partial differential equation of out-of-plane motion of the plate is derived by Newton’s second law. The finite difference method in spatial field is applied to the differential equation to study the instability due to flutter and divergence. The finite difference method in both spatial and temporal field is used in the analysis of a nonlinear partial differential equation to detect bifurcations and chaos of a nonlinear forced vibration of the system. Numerical results show that, with the increasing axially moving speed, the increasing excitation amplitude, and the decreasing viscosity coefficient, the equilibrium loses its stability and bifurcates into periodic motion, and then the periodic motion becomes chaotic motion by period-doubling bifurcation.
75 citations
TL;DR: In this paper, the stability and convergence of difference schemes for second-order ordinary and partial differential equations with a fractional time derivative were proved for the diffusion equation in one-and multidimensional domains.
Abstract: Difference schemes for second-order ordinary and partial differential equations with a fractional time derivative are considered. Stationary and nonstationary problems for the diffusion equation in one-and multidimensional domains are examined separately. The stability and convergence of the difference schemes for these equations are proved.
75 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 53 |
| 2024 | 136 |
| 2023 | 170 |
| 2022 | 357 |
| 2021 | 733 |
| 2020 | 690 |