Summarizing the Method of Solution of the Majority of Differential Equation by Using Tensor Product B-Spline Wavelet Scaling Functions in Network Security and Software Security Area, the Imitating Von Neumann Stability Analysis and a Typical Example

2009 ◽  
Author(s):  
Xiong Lei ◽  
Liu KeZhong ◽  
Zhu ZhenHuan ◽  
Wen YuanQiao ◽  
Mu JunMin ◽  
...  
Keyword(s):  
Differential Equation ◽  
Stability Analysis ◽  
Tensor Product ◽  
Software Security ◽  
Scaling Functions ◽  
Von Neumann ◽  
B Spline ◽  
Method Of Solution ◽  
Von Neumann Stability ◽  
Von Neumann Stability Analysis

Stability of discrete schemes of Biot’s poroelastic equations

2020 ◽  
Author(s):  
Y Alkhimenkov ◽  
L Khakimova ◽  
Y Y Podladchikov
Keyword(s):  
Stability Analysis ◽  
Three Dimensions ◽  
Stability Conditions ◽  
Von Neumann ◽  
Explicit Schemes ◽  
Numerical Stability Analysis ◽  
Von Neumann Stability ◽  
Von Neumann Stability Analysis ◽  
Biot’S Equations ◽  
Implicit And Explicit

Summary The efficient and accurate numerical modeling of Biot’s equations of poroelasticity requires the knowledge of the exact stability conditions for a given set of input parameters. Up to now, a numerical stability analysis of the discretized elastodynamic Biot’s equations has been performed only for a few numerical schemes. We perform the von Neumann stability analysis of the discretized Biot’s equations. We use an explicit scheme for the wave propagation and different implicit and explicit schemes for Darcy’s flux. We derive the exact stability conditions for all the considered schemes. The obtained stability conditions for the discretized Biot’s equations were verified numerically in one-, two- and three-dimensions. Additionally, we present von Neumann stability analysis of the discretized linear damped wave equation considering different implicit and explicit schemes. We provide both the Matlab and symbolic Maple routines for the full reproducibility of the presented results. The routines can be used to obtain exact stability conditions for any given set of input material and numerical parameters.

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