Computing local solution branches with a direct method

Abstract

The well known simple bifurcation problems are considered in the paper. Using an extended system, the simple bifurcation points are first embeded, then numerically approximated as regular solutions. Finally, a direct method which is very suitable to the numerical approximation is provided here to trace the solution branches in the neighborhood of the bifurcation point. Error estimations and numerical examples are included.

Keywords:

• Bifurcation point
• solution branch
• extended system
• Newton's method

AMS(MOS)::

• 47H09
• 65J15