Tag for the usage of RSolve, RecurrenceTable, DifferenceRoot, and other functions related to difference equations.
Questions tagged [difference-equations]
343 questions
11
votes
2 answers
Finding the general formula for the sequence defined by $u_1 = 1$ and $u_{n+1} = u_n + 1 + \sqrt{u_n+3}$
Let be given sequence $(u_n)$ satisfying:
$$u_1 = 1, \quad u_{n+1} = u_n + 1 + \sqrt{u_n+3}, \forall n \geq 1.$$
I tried
ClearAll["Global`*"];
RSolve[{a[x, n + 1] == a[x, n] + 1 + Sqrt[ a[x, n] + 3],
a[x, 1] == 1}, a[x, n], n]
{{a[x, n] -> 6…
minhthien_2016
- 3,347
- 14
- 22
8
votes
3 answers
How can I solve a forward-backward-looking recurrence system?
I would like to (numerically) solve a forward-backward looking recurrence equation in Mathematica. The system is something like:
x[n+1] = x[n] + y[n]
y[n] = 2* y[n+1]
subject to
x[0]=1,y[N]=1
The problem is that the boundary of x at the…
Breugem
- 785
- 3
- 12
7
votes
2 answers
Find a stable 3-cycle of the sine map
I am trying to find an stable 3-cycle for the sine map $g(x) = a \sin(\pi x)$ but I do not know exactly how to use mathematica to do so. Is there anyone familiar with this?
$x$ lies as before between 0 and 1 but the real parameter $a$ is positive…
user65365
- 71
- 1
7
votes
0 answers
How to solve this multivariate recurrence with Mathematica?
I would like to solve this recurrence relation:
$a_{m,n}=a_{m-1,n}+a_{m,n-1}$
with
$a_{0,0}=0, a_{m,0}=1, a_{0,n}=1$ for all $m\neq0$ and $n\neq0$
That's resembles the Tartaglia/Pascal's triangle,
the solution should be just the…
skan
- 193
- 5
7
votes
3 answers
Solving coupled recursion equations for a target variable
I have a set of coupled recursion equations and want to express the final solution in terms of one of the variables:
RSolve[
{d[n] == a[n] + b[n] + c[n],
a[n] == a[n - 1] + c[n - 1],
b[n] == a[n - 1],
c[n] == b[n - 1] + c[n - 1]},
{d[n]},…
David G. Stork
- 41,180
- 3
- 34
- 96
6
votes
1 answer
RSolve[{y[0] == y0, y[t + 1] == (1 - (t + 1)/100) y[t]}, y[t], t]
When I evaluate this code:
RSolve[{y[0] == y0, y[t + 1] == (1 - (t + 1)/100) y[t]}, y[t], t]
I get an RSolve::bvnul error. I don't understand why.
Yet, if I run this code, I get the sequence I want.
FoldList[#1 (1 - #2) &, 1, Range[1/100, 1,…
Seth Chandler
- 3,132
- 14
- 25
6
votes
6 answers
Recursion question
The first two terms of a sequence are $a_1 = 1$ and $a_2 = \frac {1}{\sqrt3}$. For $n\ge1$,
$$a_{n + 2} = \frac {a_n + a_{n + 1}}{1 - a_na_{n + 1}}.$$
What is $|a_{2009}|$?
So I tried (thanks to Paul Wellin):
fun[n_] := Module[{prev = 1, this =…
David
- 14,883
- 4
- 44
- 117
4
votes
1 answer
RSolve Lotka-Volterra: A Closed Form Solution to this Difference Equation?
I would like to solve a difference equation, a Lotka-Volterra difference equation.
I tried a model from
http://www.stolaf.edu/people/mckelvey/envision.dir/nonDE.lotka-volt.html
Using their parameters:
a = 0.04; b = 0.0005; c = 0.2; d = 0.1;
I…
Laura
- 61
- 2
4
votes
1 answer
Solving recurrent equations with RSolve
I need to find (or guess?) the symbolic functional form of aFun[n] for a general n (where n>=1). Anyone can help?
aFun[n_] :=
Block[
{a},
a[-1, 0] = 0;
a[n + 1, 0] = 0;
a[-1, 1] = 0;
a[n + 1, 1] = 0;
With[{eqs =
Table[{a[i, 0] ==…
Monire Jalili
- 315
- 1
- 7
4
votes
2 answers
Using RSolve for recurrence equation
I'd like to use Mathematica to verify the solution to a recurrence equation. I have the following equation:
$Q_{k+1} = Q_k + \alpha(r_{k+1} - Q_k)$.
I also have a derivation showing how to obtain a solution for any $k$:
$Q_k = Q_{k-1} + \alpha(r_k -…
whaaswijk
- 43
- 4
3
votes
1 answer
MAP a business cycles model
There is a Business Cycles Map on Phaser 3.0 and I've trying to run it on Mathematica the last four days without succes.
The equations are
$$
x_1 = (1.0 - a s)x_1 + a \left[s m + g \left(\frac{s m}{d} - x_2\right) + \mathrm{atan}(x_1 -…
user6983
3
votes
2 answers
RecurrenceTable with a recurrence function of two variables
I have to calculate the cool down process of a regenerative heat exchanger. I solved the problem in Excel before, but now I want to do it with Mathematica. I want to create a table with the variables t and z. For t = 0, there is a function which…
Daniel
- 33
- 3
3
votes
2 answers
Need help formatting `DifferenceRoot` for LaTeX
I want to put this into LaTeX format. What do I do?
(FindSequenceFunction[Join[{5, 3, 3, 2}, Table[2, {80}]], k + 1] + n - 1)
-1 + n + DifferenceRoot[Function[{[FormalY], [FormalN]}, {16 - 8 [FormalN] + (3 - [FormalN]) [FormalY][[FormalN]] +…
Fred Daniel Kline
- 2,360
- 2
- 20
- 41
3
votes
3 answers
How to draw discrete dynamic systems in mathematica
How to find invariant sets in nonlinear discrete dynamical systems. How to draw discrete dynamic systems in mathematica?
$$x[n+1]=f(x[n],y[n]), y[n+1]=g(x[n],y[n])$$
example…
Zafar
- 61
- 2
3
votes
0 answers
Compute the sum given a recursion for each summand
I have a system of two recursive equations with two unknowns A[n] and B[n] which apparently Mathematica can't solve
RSolve not evaluating when given my system of recurrence equations
Each $A[n]$ is a polynomial divided by a Pochhammer symbol: $A[n]…
Reimundo Heluani
- 141
- 3