6533b821fe1ef96bd127ac5f

RESEARCH PRODUCT

A Singular Multi-Grid Iteration Method for Bifurcation Problems

H. Weber

subject

Nonlinear systemTranscritical bifurcationIterative methodPower iterationSingular solutionComputer scienceFixed-point iterationMathematicsofComputing_NUMERICALANALYSISApplied mathematicsBifurcation diagramBifurcation

description

We propose an efficient technique for the numerical computation of bifurcating branches of solutions of large sparse systems of nonlinear, parameter-dependent equations. The algorithm consists of a nested iteration procedure employing a multi-grid method for singular problems. The basic iteration scheme is related to the Lyapounov-Schmidt method and is widely used for proving the existence of bifurcating solutions. We present numerical examples which confirm the efficiency of the algorithm.

yearjournalcountryeditionlanguage
1984-01-01
https://doi.org/10.1007/978-3-0348-6256-1_38