Can this be turned into a differential equation? Recursive diffy Q?

Click For Summary

Discussion Overview

The discussion revolves around the possibility of converting a recursive energy loss function into a differential equation. Participants explore the implications of a device losing 3% of its energy each time it is turned on, starting from 100% energy, and consider whether this behavior can be modeled continuously rather than discretely.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant presents a recursive function to describe energy loss, questioning if it can be represented as a differential equation.
  • Another participant argues against the possibility of forming a differential equation, citing the discrete nature of the energy loss at specific intervals.
  • A third participant proposes an alternative recursive formula that appears to express the same concept, suggesting a pattern in the energy loss.
  • A later reply introduces the idea of a delay differential equation, referencing external material for further context.

Areas of Agreement / Disagreement

Participants do not reach a consensus on whether the recursive function can be transformed into a differential equation, with differing views on the nature of the energy loss process.

Contextual Notes

The discussion highlights the limitations of modeling discrete processes with continuous equations, as well as the potential for different interpretations of the recursive relationships involved.

DrummingAtom
Messages
657
Reaction score
2
Let's say you have a loss of 3% of the current energy on a device for every time is gets turned on. It starts at a 100% energy.

The only way I could think of it is a recursive function. Here's what I came up:

E(t) = Et - .03*Et-1

E(0) = 1

E(1) = 1 - .03*E0

E(2) = E1 - .03*E1

...

Where E = Energy and t = each time turned on.

I feel like the solution should be something close to E-.03t but it's not. I know the recursive function describes it exactly but I have to wonder if it's even possible to turn this into a differential equation?

Thanks.
 
Physics news on Phys.org
I don't think so considering you are look at specifc steps(each time you turn it on and off) and not a continuous interval..
 
Let me propose an alternative recursive formula (it should be obvious why this is the same)
E1 = .97 E0=.97
E2 = .97 E1=.972
 

Similar threads

Undergrad Proving a basis is a basis for homogeneous linear differential equation with constant (complex) coefficients
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Differential equation and Appell polynomials
  • · Replies 1 ·
Replies
1
Views
4K
Undergrad Differential Equations For Solving A Recursive equation
  • · Replies 5 ·
Replies
5
Views
5K
Undergrad Verifying properties of Green's function
  • · Replies 1 ·
Replies
1
Views
4K
Undergrad On error estimates of approximate solutions
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad Solving Recursive Equations: Logistic Equation
  • · Replies 19 ·
Replies
19
Views
3K
Undergrad Solving and manipulating the damped oscillator differential equation
  • · Replies 6 ·
Replies
6
Views
3K
Undergrad Why Lagrange’s method of solving Pp + Qq=R works?
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad On sub and super solutions: Teschl and others
  • · Replies 5 ·
Replies
5
Views
4K
Undergrad Second order non-homogeneous linear ordinary differential equation
  • · Replies 2 ·
Replies
2
Views
3K