On the stability regions of multistep multiderivative methods

1978 ◽  
pp. 63-80 ◽  
Author(s):  
Rolf Jeltsch
Keyword(s):  
Stability Regions ◽  
The Stability ◽  
Multiderivative Methods

A Quasiperiodic Mathieu Equation

1995 ◽  
Author(s):  
Richard Rand ◽  
Rachel Hastings
Keyword(s):  
Numerical Integration ◽  
Mathieu Equation ◽  
Stability Regions ◽  
Regions Of Stability ◽  
Extensive Computation ◽  
The Stability ◽  
Direct Numerical Integration

Abstract In this work we investigate the following quasiperiodic Mathieu equation: x ¨ + ( δ + ϵ cos ⁡ t + ϵ cos ⁡ ω t ) x = 0 We use numerical integration to determine regions of stability in the δ–ω plane for fixed ϵ. Graphs of these stability regions are presented, based on extensive computation. In addition, we use perturbations to obtain approximations for the stability regions near δ=14 for small ω, and we compare the results with those of direct numerical integration.

scholarly journals LOCATION AND STABILITY OF THE TRIANGULAR POINTS IN THE TRIAXIAL ELLIPTIC RESTRICTED THREE-BODY PROBLEM

2021 ◽  
Vol 57 (2) ◽  
pp. 311-319
Author(s):  
M. Radwan ◽  
Nihad S. Abd El Motelp
Keyword(s):  
Linear Stability ◽  
Periodic Orbits ◽  
Body Problem ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Stability Regions ◽  
Triangular Points ◽  
Problem Frame ◽  
The Stability ◽  
Three Body

The main goal of the present paper is to evaluate the perturbed locations and investigate the linear stability of the triangular points. We studied the problem in the elliptic restricted three body problem frame of work. The problem is generalized in the sense that the two primaries are considered as triaxial bodies. It was found that the locations of these points are affected by the triaxiality coefficients of the primaries and the eccentricity of orbits. Also, the stability regions depend on the involved perturbations. We also studied the periodic orbits in the vicinity of the triangular points.

PHASE INSTABILITIES OF DISTORTED HEXAGONAL PATTERNS

2001 ◽  
Vol 11 (11) ◽  
pp. 2771-2777
Author(s):  
B. PEÑA ◽  
C. PÉREZ–GARCÍA
Keyword(s):  
Analytical Study ◽  
Full Range ◽  
Amplitude Equation ◽  
Phase Equation ◽  
Stability Regions ◽  
The Stability ◽  
Phase Instabilities

We present an analytical study on the stability of distorted hexagonal patterns. From a general amplitude equation we calculate the instabilities with respect to homogeneous and longwave perturbations. The latter lead to the phase equations that permit to determine the stability regions. Slightly squeezed hexagons are locally stable in a full range of distortion angles. The stability regions obtained from the phase equation are similar to those obtained numerically by other authors [Gunaratne et al., 1994].

scholarly journals Boundary Criteria for the Stability of Delay Differential-Algebraic Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
Leping Sun ◽  
Yuhao Cong
Keyword(s):  
Asymptotic Stability ◽  
Differential Algebraic Equations ◽  
Analytical Function ◽  
Algebraic Equations ◽  
Stability Criteria ◽  
Stability Regions ◽  
The Stability ◽  
Delay Differential

This paper is concerned with the asymptotic stability of delay differential-algebraic equations. Two stability criteria described by evaluating a corresponding harmonic analytical function on the boundary of a certain region are presented. Stability regions are also presented so as to show the method geometrically. Our results are not reported.

Asymptotic Stability Of Dynamic Equations With Two Fractional Terms: Continuous Versus Discrete Case

2015 ◽  
Vol 18 (2) ◽  
Author(s):  
Jan Čermák ◽  
Tomáš Kisela
Keyword(s):  
Asymptotic Stability ◽  
Fractional Derivatives ◽  
Fractional Difference ◽  
Caputo Fractional Derivatives ◽  
Stability Regions ◽  
The Stability ◽  
Fractional Terms ◽  
Discrete Stability ◽  
Stability Sets ◽  
Asymptotic Stability Conditions

AbstractThe paper discusses asymptotic stability conditions for the linear fractional difference equation∇with real coefficients a, b and real orders α > β > 0 such that α/β is a rational number. For given α, β, we describe various types of discrete stability regions in the (a, b)-plane and compare them with the stability regions recently derived for the underlying continuous patternDinvolving two Caputo fractional derivatives. Our analysis shows that discrete stability sets are larger and their structure much more rich than in the case of the continuous counterparts.

Computation of stability regions for the cylindrical ion trap with no octupole electric field as compared to the corresponding results of the Paul trap

2017 ◽  
Vol 23 (5) ◽  
pp. 272-279
Author(s):  
Houshyar Noshad ◽  
Majid Amouhashemi
Keyword(s):  
Electric Field ◽  
Electric Potential ◽  
Ion Trap ◽  
Paul Trap ◽  
Height Ratio ◽  
Stability Regions ◽  
Stability Diagrams ◽  
Quadrupole Component ◽  
Cylindrical Ion Trap ◽  
The Stability

The cylindrical ion trap is analyzed so that the octupole component of the electric field inside the trap is set to zero. As a consequence, the diameter to height ratio is computed to be 1.20 for which the quadrupole component of the cylindrical ion trap is dominant. Afterwards, it is concluded that the electric potential inside the trap as well as the corresponding stability regions are very similar to those obtained for an ideal Paul trap with pure quadrupole electric field. Furthermore, we drew a conclusion that the stability diagrams of the cylindrical ion trap without octupole term and the stability diagrams of the Paul trap have 5.6%, 3.7%, and 2.9% discrepancy for the first, second, and third stability diagrams, respectively. It should be noted that, expansion of the electric potential inside the cylindrical ion trap in terms of the multipole electric field components and making the advantages of the octupole term elimination has not been reported in the literature previously.

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