Euler's Method

Euler's Method is obtained by truncating the series after the second term, i.e.

,

with and in the interval .

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The algorithm can then be written as:

1 ;

2 repeat for increasing until :

.

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Worksheet 8 contained examples of use of Euler's method and also illustrates the graphical interpretation. Here, we discuss some of the theoretical aspects. First we need some preliminary results.

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Lemma

Lemma

Theorem 21

Example

Theorem 22 (Round-off error)

Example