Numerical Analysis of Ordinary Differential Equations

2015 ◽  
pp. 1053-1059
Author(s):  
Ernst Hairer ◽  
Christian Lubich
Keyword(s):  
Numerical Analysis ◽  
Differential Equations ◽  
Ordinary Differential Equations

HYPERCHAOS IN A MODIFIED CANONICAL CHUA'S CIRCUIT

2004 ◽  
Vol 14 (01) ◽  
pp. 221-243 ◽  
Author(s):  
K. THAMILMARAN ◽  
M. LAKSHMANAN ◽  
A. VENKATESAN
Keyword(s):  
Numerical Analysis ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Laboratory Experiments ◽  
System Parameter ◽  
Piecewise Linear ◽  
Electrical Circuit ◽  
First Order ◽  
Regular Behavior ◽  
Linear Elements

In this paper, we present the hyperchaos dynamics of a modified canonical Chua's electrical circuit. This circuit, which is capable of realizing the behavior of every member of the Chua's family, consists of just five linear elements (resistors, inductors and capacitors), a negative conductor and a piecewise linear resistor. The route followed is a transition from regular behavior to chaos and then to hyperchaos through border-collision bifurcation, as the system parameter is varied. The hyperchaos dynamics, characterized by two positive Lyapunov exponents, is described by a set of four coupled first-order ordinary differential equations. This has been investigated extensively using laboratory experiments, Pspice simulation and numerical analysis.

scholarly journals The Treatment of Second Order Ordinary Differential Equations Using Equidistant One-step Block Hybrid

2019 ◽  
pp. 1-9
Author(s):  
Y. Skwame ◽  
J. Sabo ◽  
M. Mathew
Keyword(s):  
Numerical Analysis ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Initial Value Problems ◽  
Second Order ◽  
Direct Solution ◽  
Block Method ◽  
Initial Value ◽  
One Step ◽  
Better Than

A general one-step hybrid block method with equidistant of order 6 has been successfully developed for the direct solution of second order IVPs in this article. Numerical analysis shows that the developed method is consistent and zero-stable which implies its convergence. The analysis of the new method is examined on two highly and mildly stiff second-order initial value problems to illustrate the efficiency of the method. It is obvious that our method performs better than the existing method within which we compare our result with. Hence, the approach is an adequate one for solving special second order IVPs.

scholarly journals On the Numerical Analysis and Visualisation of Implicit Ordinary Differential Equations

2019 ◽  
Vol 14 (2) ◽  
pp. 281-293
Author(s):  
Elishan Braun ◽  
Werner M. Seiler ◽  
Matthias Seiß
Keyword(s):  
Numerical Analysis ◽  
Differential Equations ◽  
Ordinary Differential Equations

NUMERICAL ANALYSIS AND CONTROL OF BIFURCATION PROBLEMS (II): BIFURCATION IN INFINITE DIMENSIONS

1991 ◽  
Vol 01 (04) ◽  
pp. 745-772 ◽  
Author(s):  
EUSEBIUS DOEDEL ◽  
HERBERT B. KELLER ◽  
JEAN PIERRE KERNEVEZ
Keyword(s):  
Numerical Analysis ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Software Package ◽  
Infinite Dimensions ◽  
Bifurcation Phenomena ◽  
Bifurcation Problems ◽  
And Control

A number of basic algorithms for the numerical analysis and control of bifurcation phenomena are described. The emphasis is on algorithms based on pseudoarclength continuation for ordinary differential equations. Several illustrative examples computed with the AUTO software package are included. This is Part II of the paper that appeared in the preceding issue [Doedel et al., 1991] and that mainly dealt with algebraic problems.

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