Variability of local stress states resulting from the application of Monte Carlo and finite difference methods to the stability study of a selected slope

2018 ◽  
Vol 245 ◽  
pp. 370-389 ◽  
Author(s):  
Antonio Pasculli ◽  
Monia Calista ◽  
Nicola Sciarra
Keyword(s):  
Monte Carlo ◽  
Finite Difference ◽  
Finite Difference Methods ◽  
Local Stress ◽  
Stability Study ◽  
Difference Methods ◽  
Stress States ◽  
The Stability

scholarly journals Stability and Convergence of Two-Step Obrechkoff Scheme For Second-Order Two-Point Boundary Value Problem

2017 ◽  
Vol 4 (1) ◽  
Author(s):  
Olufemi Bosede ◽  
Ashiribo Wusu ◽  
Moses Akanbi
Keyword(s):  
Mathematical Modeling ◽  
Differential Equation ◽  
Finite Difference ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Finite Difference Methods ◽  
Stability And Convergence ◽  
Point Boundary ◽  
Difference Methods ◽  
The Stability

Mathematical modeling of scientific and engineering processes often yield Boundary Value Problems (BVPs). One of the broad categories of numerical methods for solving BVPs is the finite difference methods, in which the differential equation is replaced by a set of difference equations which are solved by direct or iterative methods. In this paper, we use some properties of matrices to analyze the stability and convergence of the prominent finite difference methods - two-step Obrechkoff method - for solving the boundary value problem $u^{\prime \prime} = f(t,u)$, $a < x < b$, $u(a) = \eta_1$, $u(b) = \eta_2$. Conditions for the stability and convergence of the two-step Obrechkoff method method were established.

scholarly journals Classical and Multisymplectic Schemes for Linearized KdV Equation: Numerical Results and Dispersion Analysis

Fluids ◽  
2021 ◽  
Vol 6 (6) ◽  
pp. 214
Author(s):  
Adebayo Abiodun Aderogba ◽  
Appanah Rao Appadu
Keyword(s):  
Finite Difference ◽  
Numerical Experiments ◽  
Stability Region ◽  
Kdv Equation ◽  
Finite Difference Methods ◽  
Dispersion Analysis ◽  
Explicit Scheme ◽  
Difference Methods ◽  
Relative Errors ◽  
The Stability

We construct three finite difference methods to solve a linearized Korteweg–de-Vries (KdV) equation with advective and dispersive terms and specified initial and boundary conditions. Two numerical experiments are considered; case 1 is when the coefficient of advection is greater than the coefficient of dispersion, while case 2 is when the coefficient of dispersion is greater than the coefficient of advection. The three finite difference methods constructed include classical, multisymplectic and a modified explicit scheme. We obtain the stability region and study the consistency and dispersion properties of the various finite difference methods for the two cases. This is one of the rare papers that analyse dispersive properties of methods for dispersive partial differential equations. The performance of the schemes are gauged over short and long propagation times. Absolute and relative errors are computed at a given time at the spatial nodes used.

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