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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.


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Journal ArticleDOI
TL;DR: Two high-accuracy finite-difference schemes for simulating long-range linear wave propagation are presented: a maximum-order scheme and an optimized scheme that combines a seven-point spatial operator and an explicit six-stage low-storage time-march method of Runge--Kutta type.
Abstract: Two high-accuracy finite-difference schemes for simulating long-range linear wave propagation are presented: a maximum-order scheme and an optimized scheme. The schemes combine a seven-point spatial operator and an explicit six-stage low-storage time-march method of Runge--Kutta type. The maximum-order scheme can accurately simulate the propagation of waves over distances greater than five hundred wavelengths with a grid resolution of less than twenty points per wavelength. The optimized scheme is found by minimizing the maximum phase and amplitude errors for waves which are resolved with at least ten points per wavelength, based on Fourier error analysis. It is intended for simulations in which waves travel under three hundred wavelengths. For such cases, good accuracy is obtained with roughly ten points per wavelength.

120 citations

Posted Content
TL;DR: In this article, a one dimensional fractional diffusion model with the Riemann-Liouville fractional derivative is studied, and an unconditionally stable weighted average finite difference method is derived.
Abstract: A one dimensional fractional diffusion model with the Riemann-Liouville fractional derivative is studied. First, a second order discretization for this derivative is presented and then an unconditionally stable weighted average finite difference method is derived. The stability of this scheme is established by von Neumann analysis. Some numerical results are shown, which demonstrate the efficiency and convergence of the method. Additionally, some physical properties of this fractional diffusion system are simulated, which further confirm the effectiveness of our method.

120 citations

Journal ArticleDOI
TL;DR: In this article, a singular mapping for nonlinear degenerate parabolic convection-diffusion equations is proposed, where the nonlinear convective flux function has a discontinuous coefficient γ(x) and the diffusion function A(u) is allowed to be strongly degenerate.
Abstract: We analyze approximate solutions generated by an upwind difference scheme (of Engquist-Osher type) for nonlinear degenerate parabolic convection-diffusion equations where the nonlinear convective flux function has a discontinuous coefficient γ(x) and the diffusion function A(u) is allowed to be strongly degenerate (the pure hyperbolic case is included in our setup). The main problem is obtaining a uniform bound on the total variation of the difference approximation u Δ , which is a manifestation of resonance. To circumvent this analytical prob- lem, we construct a singular mapping Ψ(γ,·) such that the total variation of the transformed variable z Δ =Ψ ( γ Δ ,u Δ ) can be bounded uniformly in Δ. This establishes strong L 1 com- pactness of z Δ and, since Ψ(γ,·) is invertible, also u Δ . Our singular mapping is novel in that it incorporates a contribution from the diffusion function A(u). We then show that the limit of a converging sequence of difference approximations is a weak solution as well as satisfying a Kruzkov-type entropy inequality. We prove that the diffusion function A(u )i s Hcontin- uous, implying that the constructed weak solution u is continuous in those regions where the diffusion is nondegenerate. Finally, some numerical experiments are presented and discussed.

120 citations

Journal ArticleDOI
TL;DR: In this paper, the authors presented a numerical solution for the flow of a Newtonian fluid over an impermeable stretching sheet with a power law surface velocity, slip velocity and variable thickness.
Abstract: This article presents a numerical solution for the flow of a Newtonian fluid over an impermeable stretching sheet with a power law surface velocity, slip velocity and variable thickness. The flow is caused by a nonlinear stretching of a sheet. The governing partial differential equations are transformed into a nonlinear ordinary differential equation which is using appropriate boundary conditions for various physical parameters. The numerical solutions of the resulting nonlinear ODEs are found by using the efficient finite difference method (FDM). The effects of the slip parameter and the wall thickness parameter on the flow profile are presented. Moreover, the local skin friction is presented. Comparison of the obtained numerical results is made with previously published results in some special cases, and excellent agreement is noted. The results attained in this paper confirm the idea that FDM is a powerful mathematical tool and can be applied to a large class of linear and nonlinear problems arising in different fields of science and engineering.

120 citations

Journal ArticleDOI
TL;DR: In this article, the effects of viscous dissipation and stress work on the MHD forced convection adjacent to a nonisothermal wedge is numerically analyzed using the Keller box method.

120 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023125
2022320
2021724
2020681
2019667
2018694