Difference Equation versus Differential Equation

Requires a Wolfram Notebook System
Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.
Let be a generic point in the plane. The figure illustrates the relation between the difference equation
and the differential equation
for the particular case
. For decreasing values of the step size parameter
and for a chosen initial value
, you can see how the discrete process
(in white) tends to follow the trajectory of the differential equation that goes through
(in black). The background is colored using the norm of the expected motion, rescaled to be in the interval
.
Contributed by: Luis R. Izquierdo and Segismundo S. Izquierdo (March 2011)
Open content licensed under CC BY-NC-SA
Snapshots
Details
detailSectionParagraphPermanent Citation
"Difference Equation versus Differential Equation"
http://demonstrations.wolfram.com/DifferenceEquationVersusDifferentialEquation/
Wolfram Demonstrations Project
Published: March 7 2011