Gyula Farkas

7102929952

Publications - 5

A numerical C1-shadowing result for retarded functional differential equations

Gyula Farkas

Publication Name: Journal of Computational and Applied Mathematics

Publication Date: 2002-08-15

Volume: 145

Issue: 2

Page Range: 269-289

Description:

The aim of the present paper is to give a numerical C1-shadowing between the exact solutions of a functional differential equation and its numerical approximations. The shadowing result is obtained by comparing exact solutions with numerical approximation which do not share the same initial value. Behavior of stable manifolds of functional differential equations under numerics will follow from the shadowing result. © 2001 Elsevier Science B.V. All rights reserved.

Open Access: Yes

DOI: 10.1016/S0377-0427(01)00581-7

Nonexistence of uniform exponential dichotomies for delay equations

Gyula Farkas

Publication Name: Journal of Differential Equations

Publication Date: 2002-06-10

Volume: 182

Issue: 1

Page Range: 266-268

Description:

No description provided

Open Access: Yes

DOI: 10.1006/jdeq.2001.4156

Conjugacy in the discretized fold bifurcation

Gyula Farkas

Publication Name: Computers and Mathematics with Applications

Publication Date: 2002-01-01

Volume: 43

Issue: 8-9

Page Range: 1027-1033

Description:

In this paper, we construct a conjugacy between the time-1-map of the solution flow generated by an ordinary differential equation and its numerical approximation in a neighborhood of a fold bifurcation point. Our main result is that the conjugacy is O(hp)-close to the identity on the center manifold where h is the step size and p is the order of the numerical method. © 2002 Elsevier Science Ltd. All rights reserved.

Open Access: Yes

DOI: 10.1016/S0898-1221(02)80011-6

Small delay inertial manifolds under numerics: A numerical structural stability result

George R. Sell Gyula Farkas

Publication Name: Journal of Dynamics and Differential Equations

Publication Date: 2002-01-01

Volume: 14

Issue: 3

Page Range: 549-588

Description:

In this paper we formulate a numerical structural stability result for delay equations with small delay under Euler discretization. The main ingredients of our approach are the existence and smoothness of small delay inertial manifolds, the C1-closeness of the small delay inertial manifolds and their numerical approximation and M.-C. Li's recent result on numerical structural stability of ordinary differential equations under the Euler method. © 2002 Plenum Publishing Corporation.

Open Access: Yes

DOI: 10.1023/A:1016335115301

Stability properties of positive solutions to partial differential equations with delay

Gyula Farkas Peter L. Simo

Publication Name: Electronic Journal of Differential Equations

Publication Date: 2001-12-01

Volume: 2001

Issue: Unknown

Page Range: XCXXI-XCXXII

Description:

We investigate the stability of positive stationary solutions of semilinear initial-boundary value problems with delay and convex or concave nonlinearity. If the nonlinearity is monotone, then in the convex case /(O) < 0 implies instability and in the concave case /(O) > 0 implies stability. Special cases are shown where the monotonicity assumption can be weakened or omitted. ©2001 Southwest Texas State University.

Open Access: Yes

DOI: DOI not available