An Optimal Finite Difference Scheme with Minimized Dispersion and Adaptive Dissipation Considering the Spectral Properties of the Fully Discrete Scheme

2021 ◽  
Vol 89 (2) ◽  
Author(s):  
Zhensheng Sun ◽  
Yu Hu ◽  
Yuxin Ren ◽  
Kai Mao
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Spectral Properties ◽  
Discrete Scheme ◽  
Fully Discrete

scholarly journals INVESTIGATION OF A COST‐EFFECTIVE FINITE DIFFERENCE SCHEME FOR THE TRANSPORT EQUATION

2003 ◽  
Vol 8 (3) ◽  
pp. 247-258
Author(s):  
D. G. Slugin ◽  
A. V. Popov
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Transport Equation ◽  
Finite Difference Scheme ◽  
Three Dimensional ◽  
Cost Effective ◽  
Differential Approximation ◽  
Fully Discrete ◽  
Implicit Finite Difference Scheme ◽  
Implicit Finite Difference

The transport equation for three‐dimensional flow of a viscous gas is considered. An implicit finite difference scheme is constructed for approximating the transport equation. The error estimation is proved. The main part of the analysis is done for the first differential approximation of the proposed finite difference scheme, but the results are also valid in the fully discrete case.

scholarly journals The convergence of a numerical method for total variation flow

2021 ◽  
Vol 15 ◽  
pp. 174830262110113
Author(s):  
Qianying Hong ◽  
Ming-jun Lai ◽  
Jingyue Wang
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Numerical Method ◽  
Convergence Analysis ◽  
Total Variation ◽  
Iterative Algorithm ◽  
Finite Difference Scheme ◽  
Gradient Flow ◽  
Time Dependent ◽  
Total Variation Flow

We present a convergence analysis for a finite difference scheme for the time dependent partial different equation called gradient flow associated with the Rudin-Osher-Fetami model. We devise an iterative algorithm to compute the solution of the finite difference scheme and prove the convergence of the iterative algorithm. Finally computational experiments are shown to demonstrate the convergence of the finite difference scheme.

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