Euler's Method for the Exponential Function

x

1.

approximation step

3

For each value of

x

, the sequence

e

n

(x)=

n

1+

x

n

converges to

x

e

. Also, if

E

n

(t)

is the Euler method approximation to the solution of the differential equation

y'=y

,

y(0)=1

on the interval

[0,x]

with

h=x/n

, then

E

n

(t)

(the red curve) converges to

t

e

for each

t

in the interval. The points generated by Euler's method are marked in green. Observe that for any

n

, the error between the approximation and the real value increases with the value of

x

.

External Links

Exponential Function (Wolfram MathWorld)

Euler's Method (Wolfram MathWorld)

Permanent Citation

Arnaud Crouzet

"Euler's Method for the Exponential Function"
http://demonstrations.wolfram.com/EulersMethodForTheExponentialFunction/
Wolfram Demonstrations Project
Published: March 7, 2011