Questions tagged [difference-equations]
Tag for the usage of RSolve, RecurrenceTable, DifferenceRoot, and other functions related to difference equations.
369 questions
5
votes
3
answers
292
views
Is there an equivalent of Exponent for difference equations?
[Edited.]
For $ax^{2}+bx+c$, I can write
poly = a x^2 + b x + c;
Exponent[poly, x]
and get back 2.
I don't see a built-in ...
- 667
0
votes
0
answers
40
views
Inconsistent recurrence relation for Weierstrass sigma function double series between MathWorld and DLMF
There is a curious recurrence relation for double series of Weierstrass sigma function listed at DLMF defition 23.9.8
$$
a_{m,n} = 3(m+1) a_{m+1,n-1} + \frac{16}{3}(n+1) a_{m-2,n+1} - \frac{1}{3}(2m+...
- 694
0
votes
0
answers
89
views
Error in Lyapunov Exponent
I want to calculate Lyapunov exponents for by varying two parameters so that I can get density plot.
I am using the code:
...
- 313
2
votes
1
answer
224
views
Generate a Table for the Onset of Period Doubling for the Sine Map
Below is my Mathematica code to generate the bifurcation diagram of the sine map x_n+1 = rsin(Pix_n) or in this form f(x) = rsin(Pix). (How to isolate the bifurcation points from the sine map's ...
- 2,027
0
votes
0
answers
88
views
How does Mathematica deal with undefined lists in equations?
I'm trying to solve the following recurrence equations, vP = tail(v)∧ wP= w ⊗ head(v), and get its invariant relation, where the variables are of ListType v,w and ...
- 1
3
votes
3
answers
371
views
How to isolate the bifurcation points from the sine map's bifurcation diagram
I have the following code for the bifurcation diagram of the sine map. It works well but I would like to isolate where the onset of period doubling begins (the bifurcation points) along the horizontal ...
- 2,027
1
vote
3
answers
163
views
Find the general term formula for sequence $a_1 + 3 a_2 + \cdots + (2 n - 1) a_n = 2 n$
Given:
a[1] + 3 a[2] + ... + (2 n - 1) a[n] == 2 n
I want to find a[n]. I tried RSolve, but ...
user105429
3
votes
1
answer
167
views
StateSpaceModel for second-order difference equation
I'm reading an introductory chapter on Linear state space with python in here.
As an example, they consider the following equation:
$$
y_{t+1} = \phi_0 + \phi_1 y_t + \phi_2 y_{t-1}
\quad \text{s.t.} ...
- 5,017
5
votes
2
answers
214
views
Expression for a vector-valued recurrence relation
I am trying to find an expression for the x[t+1] in the following recurrence relation
x[t + 1] == x[t]/P . x[t]
Where ...
- 8,789
14
votes
0
answers
384
views
RSolve give a wrong result?
Bug introduced at or before 5.2, persisting through 14.2
I am trying to solve the recurrence solution:
$$
a_{n+1}=a_{n}+2+2\sqrt{a_{n}} \tag1
$$
and the following is my Mathematica code:
...
- 521
0
votes
1
answer
107
views
0
votes
1
answer
156
views
0
votes
0
answers
100
views
How to solve numerically a fourth order BVP having a Boundary condition at Limit Approaches to 0
I have the following fourth order BVP (pde):
$\frac{1}{4}f_{yyt}+H^{4}(ff_{yyy}-f_{y}f_{yy})=\frac{1}{H^{2}R}(yf_{yyy}+2f_{yy})$
with boundary conditions:
$f(0,t)=0$, $f(1,t)=0$, $f_{y}(1,t)=-\frac{\...
- 83
2
votes
0
answers
85
views
Recurrence relation of the type X[n1+1,n2] + X[n1-1,n2] + X[n1,n2+1] + X[n1,n2-1] = q X[n1,n2]. RSolve not OK
I need to solve a recurrence relation of the type
X[n1+1,n2] + X[n1-1,n2] + X[n1,n2+1] + X[n1,n2-1] = q X[n1,n2]
How do I do this? RSolve does not work.
- 1,748
0
votes
0
answers
87
views
Issue solving a recurrence relation
I´m trying to solve the following recurrence relation in Mathematica:
...
- 197