### Abstract

The first part of this paper starts with a brief discussion of some methods for solution of nonlinear equations which have interested the first author over the last twenty years or so. In the second part we discuss a recent research involvement, the success of which relies heavily on the numerical solution of nonlinear equation systems. We briefly describe path-following methods and then present an application to a simple steady-state reactiondiffusion equation arising in combustion theory. Results for some regular geometric shapes are shown and compared with those from an approximate method. 7

Original language | English |
---|---|

Pages (from-to) | 55-64 |

Number of pages | 10 |

Journal | ANZIAM Journal |

Volume | 42 |

Issue number | 1 |

Publication status | Published - 2000 |

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### ASJC Scopus subject areas

- Mathematics (miscellaneous)

### Cite this

**Solution of nonlinear equations and computation of multiple solutions of a simple reaction-diffusion equation.** / Swift, Adrian; Balakrishnan, Easwaran.

Research output: Contribution to journal › Article

*ANZIAM Journal*, vol. 42, no. 1, pp. 55-64.

}

TY - JOUR

T1 - Solution of nonlinear equations and computation of multiple solutions of a simple reaction-diffusion equation

AU - Swift, Adrian

AU - Balakrishnan, Easwaran

PY - 2000

Y1 - 2000

N2 - The first part of this paper starts with a brief discussion of some methods for solution of nonlinear equations which have interested the first author over the last twenty years or so. In the second part we discuss a recent research involvement, the success of which relies heavily on the numerical solution of nonlinear equation systems. We briefly describe path-following methods and then present an application to a simple steady-state reactiondiffusion equation arising in combustion theory. Results for some regular geometric shapes are shown and compared with those from an approximate method. 7

AB - The first part of this paper starts with a brief discussion of some methods for solution of nonlinear equations which have interested the first author over the last twenty years or so. In the second part we discuss a recent research involvement, the success of which relies heavily on the numerical solution of nonlinear equation systems. We briefly describe path-following methods and then present an application to a simple steady-state reactiondiffusion equation arising in combustion theory. Results for some regular geometric shapes are shown and compared with those from an approximate method. 7

UR - http://www.scopus.com/inward/record.url?scp=33747312018&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33747312018&partnerID=8YFLogxK

M3 - Article

VL - 42

SP - 55

EP - 64

JO - ANZIAM Journal

JF - ANZIAM Journal

SN - 1446-1811

IS - 1

ER -