#### Document Type

Article

#### Publication Date

2009

#### Abstract

Many applications give rise to separable parameterized equations, which have the form *A*(*y*, *µ*)*z* + *b*(*y, µ*) = 0, where *z* ∈ **R*** ^{N}* ,

*y*∈

**R**

*,*

^{n}*µ*∈

**R**

*, and the (*

^{s}*N*+

*n*) ×

*N*matrix

*A*(

*y, µ*) and (

*N*+

*n*) vector

*b*(

*y, µ*) are

*C*

^{2}-Lipschitzian in (

*y, µ*) ∈ Ω ⊂

**R**

*×*

^{n}**R**

*. We present a technique which reduces the original equation to the form*

^{s}*f*(

*y*,

*µ*) = 0, where

*f*: Ω →

**R**

*is*

^{n}*C*

^{2}-Lipschitzian in (

*y, µ*). This reduces the dimension of the space within which the bifurcation relation occurs. We derive expressions required to implement methods to solve the reduced equation. Numerical examples illustrate the use of the technique.

#### Publication Title

Electronic Transactions on Numerical Analysis

#### Volume

34

#### First Page

31

#### Last Page

43

#### Required Publisher's Statement

Copyright 2009, Kent State University. ISSN 1068-9613

#### Recommended Citation

Shen, Yun-Qiu and Ypma, Tjalling J., "Numerical Bifurcation of Separable Parameterized Equations" (2009). *Mathematics.* Paper 91.

http://cedar.wwu.edu/math_facpubs/91