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iteration 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:
  1. Choose a convergent or a divergent function g(x).
  2. Drag the mouse along the x axis.
The diagram illustrates the process. Note how the red lines converge (or do not!) towards the solution. Such diagrams, are often called "cobweb diagrams".

Downloadable Files

If your computer is set up with Excel then you can download this file to investigate solving equations by iterative methods.
Excel - iterate01Excel - iterate01
Investigate iteration further using Excel.

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



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.


A statement that two mathematical expressions are equal.


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


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


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


the answer to a problem.

Full Glossary List

This question appears in the following syllabi:

SyllabusModuleSectionTopicExam Year
AQA A-Level (UK - Pre-2017)C3Numerical MethodsIterative methods-
AQA A2 Maths 2017Pure MathsNumerical MethodsIteration-
AQA AS/A2 Maths 2017Pure MathsNumerical MethodsIteration-
CCEA A-Level (NI)C3Numerical MethodsIterative methods-
CIE A-Level (UK)P2Numerical MethodsIterative methods-
Edexcel A-Level (UK - Pre-2017)C3Numerical MethodsIterative methods-
Edexcel A2 Maths 2017Pure MathsNumerical MethodsIteration-
Edexcel AS/A2 Maths 2017Pure MathsNumerical MethodsIteration-
OCR A-Level (UK - Pre-2017)C3Numerical MethodsIterative methods-
OCR A2 Maths 2017Pure MathsNumerical MethodsIteration-
OCR MEI A2 Maths 2017Pure MathsNumerical MethodsIteration-
OCR-MEI A-Level (UK - Pre-2017)NMNumerical MethodsIterative methods-
Pre-U A-Level (UK)8Numerical MethodsIterative methods-
Scottish Advanced HighersM3Numerical MethodsIterative methods-
Scottish (Highers + Advanced)AM3Numerical MethodsIterative methods-
Universal (all site questions)NNumerical MethodsIterative methods-
WJEC A-Level (Wales)C3Numerical MethodsIterative methods-