Towards a Systematic Linear Stability Analysis of Numerical Methods for Systems of Stochastic Differential Equations

2010 ◽  
Vol 48 (1) ◽  
pp. 298-321 ◽  
Author(s):  
Evelyn Buckwar ◽  
Cónall Kelly
Keyword(s):  
Stability Analysis ◽  
Numerical Methods ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Linear Stability ◽  
Linear Stability Analysis

LINEAR STABILITY ANALYSIS GENERALIZED TO A THERMALLY-DRIVEN FLOW

1999 ◽  
Vol 09 (02) ◽  
pp. 415-425
Author(s):  
JEAN-MICHEL CORNET ◽  
CLAUDE-HENRI LAMARQUE
Keyword(s):  
Stability Analysis ◽  
Numerical Methods ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
The Other ◽  
Basic Solution ◽  
Driven Cavity ◽  
Convective Flows ◽  
Other Hand ◽  
Thermally Driven

We intend to establish a methodology suited to the search of the first bifurcations of convective flows using a linear stability analysis so that it permits us to define a relationship between amplitude and frequency of the perturbation. We use a particular combination of various numerical methods to compute on one hand the basic solution. On the other hand the perturbation is applied to the search for the bifurcations in a thermally-driven cavity.

scholarly journals Linear Stability Analysis of Runge-Kutta Methods for Singular Lane-Emden Equations

2020 ◽  
pp. 134-140
Author(s):  
M. O. Ogunniran ◽  
O. A. Tayo ◽  
Y. Haruna ◽  
A. F. Adebisi
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Classical Method ◽  
Kutta Method ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
The Mind

Runge-Kutta methods are efficient methods of computations in differential equations, the classical Runge-Kutta method of order 4 happens to be the most popular of these methods, and most times it is attached to the mind when Runge-Kutta methods are mentioned. However, there are numerous forms of them existing in lower and higher orders of the classical method. This work investigates the linear stabilities and abilities of some selected explicit members of these Runge-Kutta methods in integrating the singular Lane-Emden differential equations. The results obtained established the ability of the classical Runge-Kutta method and why is mostly used in computations.

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