Stability Analysis of Linearly Implicit One-Step Interpolation Methods for Stiff Retarded Differential Equations

1989 ◽  
Vol 26 (5) ◽  
pp. 1158-1174 ◽  
Author(s):  
K. Strehmel ◽  
R. Weiner ◽  
H. Claus
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Interpolation Methods ◽  
One Step ◽  
Retarded Differential Equations

Stability analysis of one-step methods for neutral delay-differential equations

1988 ◽  
Vol 52 (6) ◽  
pp. 605-619 ◽  
Author(s):  
A. Bellen ◽  
Z. Jackiewicz ◽  
M. Zennaro
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Delay Differential Equations ◽  
Neutral Delay ◽  
Neutral Delay Differential Equations ◽  
One Step ◽  
Delay Differential

STABILITY ANALYSIS OF A PROPOSED SCHEME OF ORDER FIVE FOR FIRST ORDER ORDINARY DIFFERENTIAL EQUATIONS

2021 ◽  
Vol 6 (2) ◽  
pp. 898
Author(s):  
Sunday Emmanuel Fadugba ◽  
Roseline Bosede Ogunrinde ◽  
Rowland Rotimi Ogunrinde
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Step Length ◽  
Step Method ◽  
First Order ◽  
Absolute Relative Error ◽  
One Step ◽  
Test Equation ◽  
The Stability

This paper presents the stability analysis of a proposed scheme of order five (FCM) for first order Ordinary Differential Equations (ODEs). The proposed FCM is derived by means of an interpolating function of polynomial and exponential forms. The properties of FCM were discussed extensively. The linear stability of FCM in the context of the Third Order One-Step Method (TCM) and Second Order One-Step Method (SCM) for the solution of initial value problems of first order differential equations is presented. The stability region of FCM, TCM and SCM is investigated using the Dahlquist’s test equation. The numerical results obtained via FCM are compared with TCM and SCM. Moreover, by varying the step length, the accuracy and convergence of the methods in terms of the final absolute relative error are measured. The results show that FCM converges faster and more stable than its counterparts.

Stability Analysis of Extended One-Step Schemes for Stiff and Non-Stiff Delay Differential Equations

2016 ◽  
Vol 10 (5) ◽  
pp. 1705-1717 ◽  
Author(s):  
F. Ibrahim ◽  
F. A. Rihan ◽  
S. Turek
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Delay Differential Equations ◽  
One Step ◽  
Delay Differential

One-step methods for retarded differential equations with parameters

Computing ◽  
1990 ◽  
Vol 43 (4) ◽  
pp. 343-359
Author(s):  
Tadeusz Jankowski
Keyword(s):  
Differential Equations ◽  
One Step ◽  
Retarded Differential Equations

scholarly journals Stability Analysis of Distributed Order Fractional Differential Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
H. Saberi Najafi ◽  
A. Refahi Sheikhani ◽  
A. Ansari
Keyword(s):  
Stability Analysis ◽  
Characteristic Function ◽  
Differential Equations ◽  
Density Function ◽  
Robust Stability ◽  
Fractional Differential Equations ◽  
Stability Condition ◽  
Fractional Differential ◽  
The Stability ◽  
Distributed Order

We analyze the stability of three classes of distributed order fractional differential equations (DOFDEs) with respect to the nonnegative density function. In this sense, we discover a robust stability condition for these systems based on characteristic function and new inertia concept of a matrix with respect to the density function. Moreover, we check the stability of a distributed order fractional WINDMI system to illustrate the validity of proposed procedure.

scholarly journals Stability analysis of exponential Runge–Kutta methods for delay differential equations

2011 ◽  
Vol 24 (7) ◽  
pp. 1089-1092 ◽  
Author(s):  
Y. Xu ◽  
J.J. Zhao ◽  
Z.N. Sui
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Delay Differential Equations ◽  
Runge Kutta ◽  
Delay Differential
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