This applet demonstrates finding the root of an equation f(x)=0 by fixed-point iteration. For each function f(x), we can derive one or more iteration functions of the form x = g(x) by solving for x. We plot y=g(x) against the line y=x and seek to find where the lines intersect. For some of the functions g(x) this process will be successful (the process is convergent) and for some it will not.

To run the demo:

To run the demo:

- Choose a convergent or a divergent function g(x).
- Drag the mouse along the x axis.

## Downloadable Files

If your computer is set up with Excel then you can download this file to investigate
solving equations by iterative methods.

## Software/Applets used on this page

This applet forms part of "Java Number Cruncher: The Java Programmer's Guide to Numerical Computation", Prentice-Hall, by Ronald Mak, and is provided for MathsNetAlevel-plus by that author - see

Apropos-logic

Apropos-logic

## Glossary

### axis

One of two straight lines on a graph from which measurements are taken. One axis (the y axis) is vertical; the other (the x axis) is horizontal.

### equation

A statement that two mathematical expressions are equal.

### function

A rule that connects one value in one set with one and only one value in another set.

### iteration

successive repetition of a process using the result of one stage as the input for the next.

### plot

To mark a point on a graph accurately by using its coordinates.

### solution

the answer to a problem.

## This question appears in the following syllabi:

Syllabus | Module | Section | Topic | Exam Year |
---|---|---|---|---|

AQA A-Level (UK - Pre-2017) | C3 | Numerical Methods | Iterative methods | - |

AQA A2 Maths 2017 | Pure Maths | Numerical Methods | Iteration | - |

AQA AS/A2 Maths 2017 | Pure Maths | Numerical Methods | Iteration | - |

CCEA A-Level (NI) | C3 | Numerical Methods | Iterative methods | - |

CIE A-Level (UK) | P2 | Numerical Methods | Iterative methods | - |

Edexcel A-Level (UK - Pre-2017) | C3 | Numerical Methods | Iterative methods | - |

Edexcel A2 Maths 2017 | Pure Maths | Numerical Methods | Iteration | - |

Edexcel AS/A2 Maths 2017 | Pure Maths | Numerical Methods | Iteration | - |

OCR A-Level (UK - Pre-2017) | C3 | Numerical Methods | Iterative methods | - |

OCR A2 Maths 2017 | Pure Maths | Numerical Methods | Iteration | - |

OCR MEI A2 Maths 2017 | Pure Maths | Numerical Methods | Iteration | - |

OCR-MEI A-Level (UK - Pre-2017) | NM | Numerical Methods | Iterative methods | - |

Pre-U A-Level (UK) | 8 | Numerical Methods | Iterative methods | - |

Scottish Advanced Highers | M3 | Numerical Methods | Iterative methods | - |

Scottish (Highers + Advanced) | AM3 | Numerical Methods | Iterative methods | - |

Universal (all site questions) | N | Numerical Methods | Iterative methods | - |

WJEC A-Level (Wales) | C3 | Numerical Methods | Iterative methods | - |