A new modified semi-explicit difference scheme in aerodynamics

2008 ◽  
pp. 186-190
Author(s):  
Fu De-Xun ◽  
Ma Yan-Wen
Keyword(s):  
Difference Scheme ◽  
Explicit Difference Scheme

scholarly journals A class of explicit implicit alternating difference schemes for generalized time fractional Fisher equation

2021 ◽  
Vol 6 (10) ◽  
pp. 11449-11466
Author(s):  
Xiao Qin ◽  
◽  
Xiaozhong Yang ◽  
Peng Lyu
Keyword(s):  
Difference Scheme ◽  
Unconditional Stability ◽  
Difference Schemes ◽  
Stability And Convergence ◽  
Fisher Equation ◽  
Numerical Techniques ◽  
Implicit Difference Scheme ◽  
Explicit Difference Scheme ◽  
Scientific Significance ◽  
Generalized Time

<abstract><p>The generalized time fractional Fisher equation is one of the significant models to describe the dynamics of the system. The study of effective numerical techniques for the equation has important scientific significance and application value. Based on the alternating technique, this article combines the classical explicit difference scheme and the implicit difference scheme to construct a class of explicit implicit alternating difference schemes for the generalized time fractional Fisher equation. The unconditional stability and convergence with order $ O\left({\tau }^{2-\alpha }+{h}^{2}\right) $ of the proposed schemes are analyzed. Numerical examples are performed to verify the theoretical analysis. Compared with the classical implicit difference scheme, the calculation cost of the explicit implicit alternating difference schemes is reduced by almost $ 60 $%. Numerical experiments show that the explicit implicit alternating difference schemes are also suitable for solving the time fractional Fisher equation with initial weak singularity and have an accuracy of order $ O\left({\tau }^{\alpha }+{h}^{2}\right) $, which verify that the methods proposed in this paper are efficient for solving the generalized time fractional Fisher equation.</p></abstract>

scholarly journals Stability Analysis of the Explicit Difference Scheme for Richards Equation

Entropy ◽  
2020 ◽  
Vol 22 (3) ◽  
pp. 352
Author(s):  
Fengnan Liu ◽  
Yasuhide Fukumoto ◽  
Xiaopeng Zhao
Keyword(s):  
Difference Scheme ◽  
Numerical Experiments ◽  
Richards Equation ◽  
Induction Method ◽  
Explicit Difference Scheme ◽  
Time Step ◽  
The Difference ◽  
The Stability ◽  
Forward Euler ◽  
Parabolic Term

A stable explicit difference scheme, which is based on forward Euler format, is proposed for the Richards equation. To avoid the degeneracy of the Richards equation, we add a perturbation to the functional coefficient of the parabolic term. In addition, we introduce an extra term in the difference scheme which is used to relax the time step restriction for improving the stability condition. With the augmented terms, we prove the stability using the induction method. Numerical experiments show the validity and the accuracy of the scheme, along with its efficiency.

scholarly journals Simulation of 3D Wave Fields in Inhomogeneous Domain with Complex Topography Using the Lebedev Scheme

2020 ◽  
Vol 18 (4) ◽  
pp. 66-85
Author(s):  
Pavel A. Titov
Keyword(s):  
Numerical Simulation ◽  
Linear System ◽  
Difference Scheme ◽  
Physical Models ◽  
Numerical Implementation ◽  
Complex Topography ◽  
Explicit Difference Scheme ◽  
Wave Fields ◽  
Good Consistency ◽  
Simulation Results

Numerical simulation is widely used in the study of wave fields in various media. One of the methods is to divide the domain of interest into elementary volumes and build a finite-difference scheme for numerical implementation. The work assumes that the domain can have a significant curvature of the surface, therefore, the technology of generating a mesh of curved cubes is used. This mesh provides good consistency between the discrete and physical models of the domain. A parallel algorithm is proposed for the numerical solution of a 3D linear system of elasticity theory, expressed via displacement velocities and stresses, using a curvilinear mesh and an explicit difference scheme based on the Lebedev scheme. The simulation results are presented. The calculations were carried out using the resources of the SSCC SB RAS.

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