A method for the numerical determination of bifurcation states of nonlinear systems of equations

RB Simpson - SIAM Journal on Numerical Analysis, 1975 - SIAM
A numerical technique is presented for determining a simple turning point in a branch of
solutions of an algebraic system of equations depending on a scalar parameter. Results are …

An efficient algorithm for the determination of certain bifurcation points

JP Abbott - Journal of Computational and Applied Mathematics, 1978 - Elsevier
Many practical problems require information about a branch of solutions of a system of
nonlinear equations dependent upon a scalar parameter. We discuss some techniques for …

Computing bifurcation diagrams for large nonlinear variational problems

H Jarausch, W Mackens - Large Scale Scientific Computing, 1987 - Springer
We report on a method to reduce the computational effort of computing bifurcation diagrams
for large nonlinear parameterdependent systems of variational type. Included are …

Computing simple bifurcation points using a minimally extended system of nonlinear equations

G Pönisch - Computing, 1985 - dl.acm.org
Various methods have been suggested for computing simple bifurcation points. Some of
these methods greatly enlarge the dimension of the system of equations to be solved. This …

[PDF][PDF] Numerical methods for bifurcation problems

T Küpper, HD Mittelmann… - Proceedings of a …, 1983 - interval.louisiana.edu
Various quite satisfactory analytical and numerical techniques are available for analysing
bifurcation points when something about the structure is known á priori. The author …

Direction of branches bifurcating at a bifurcation point. Determination of starting points for a continuation algorithm

M Kubíček, A Klíč - Applied Mathematics and Computation, 1983 - Elsevier
The behavior of branches of solutions of a system of nonlinear algebraic equations
depending on a parameter in a neighborhood of a bifurcation point is examined. Directions …

Folds in solutions of two parameter systems and their calculation. Part I

A Jepson, A Spence - SIAM journal on numerical analysis, 1985 - SIAM
This paper is concerned with paths of turning points in solutions of nonlinear systems having
two parameters. It is well known that these paths are solutions of a particular extended …

Path-following methods in bifurcation problems

J Brindley, C Kaas-Petersen, A Spence - Physica D: Nonlinear Phenomena, 1989 - Elsevier
Analytical methods of bifurcation theory and numerical path-following methods complement
each other in many investigations of nonlinear systems. This brief “state of the art” review …

On the bifurcation diagram of discrete analogues for ordinary bifurcation problems

E Bohl, K Kirchgässner - Mathematical Methods in the Applied …, 1979 - Wiley Online Library
On the bifurcation diagram of discrete analogues for ordinary bifurcation problems Page 1
Math. Meth. in the Appl. Sci. (1979) 566-571’ 6 BG Teubner Stuttgart 1979 MOS …

Evaluation of limit and bifurcation points for algebraic equations and nonlinear boundary-value problems

M Kubíček, M Marek - Applied Mathematics and Computation, 1979 - Elsevier
A general, straightforward method for finding branching points of algebraical systems or
nonlinear boundary-value problems is presented. The technique proposed utilizes two …