All Questions
Tagged with recursion difference-equations
87
questions
2
votes
2
answers
46
views
How to fix parameter locally for iterating recursion equations
The following is a simplified version of a more detailed problem.
I have two coupled recursion equations of two variables, x and y. One equation also depends on a parameter, c:
...
- 393
1
vote
2
answers
118
views
RecurrenceTable vs For loop : they do not give the same results. Why?
I have a second-order recurrence equation that I want to plot.
I've used two different methods.
The first uses RecurrenceTable, the second uses a traditional ...
- 33
3
votes
2
answers
61
views
RSolve does not evaluate this recursion with two boundary conditions
I am using RSolve to solve for a function defined recursively, with two boundary conditions:
First boundary condition describes the relationship between $f(1)$ and $f(0)$
Second boundary condition ...
- 131
2
votes
1
answer
86
views
3
votes
1
answer
128
views
Recurrence formula evaluating with speacial counting of subscripts
Hoping to check some recurrance relationship like this
$a_1 = x$ and $a_2 = y$, with
$$
a_{2n+1} = a_{2n} a_{2n-1}
$$
and
$$
a_{2n+2} = a_{2n+1} + 4
$$
Tried
...
- 1,642
7
votes
1
answer
278
views
Recurrences related to Ramanujan's 1/pi formulas for level 10?
In the course of my research years ago, I came across three integer sequences related to Ramanujan's pi formulas but for level $10$. Their recurrence relations may be important. (Just like the level $...
- 447
0
votes
2
answers
65
views
Recurrent equation with UnitStep function using RSolve
I have the following equation to solve
$$a[n+1] = a[n] + 6 - 100\cdot \theta(a[n]-100)$$
where $\theta(x)$ is the Heaviside step function. So I tried the following
...
1
vote
1
answer
104
views
Plot of a recursive expression having a parameter
I have a recursive expression defined as
$$
h_u= (1-a)(1-b) h_{u-1} + \sum_{k=2}^{u-1} (1-a) b h_{u-1-k} - \sum_{k=2}^{u} h_{u-k} - \sum_{k=1}^{u+1} \Lambda_{u,k}
$$
where $\Lambda_{u,k} = \sum_{m=u-k+...
- 53
2
votes
1
answer
116
views
Implement recursion one step at a time with a function of more than one variable
i am trying to implement a recursive difference equation step by step, by implementing rules, similar to Rojo's method in this thread: How can I evaluate only a single step of a recursive function?
...
- 23
1
vote
0
answers
93
views
Solving a 2D recurrence diagonal-by-diagonal
I have a 3D recurrence relation -- which I know can be hard for Mathematica to work with, so I boiled it down to 2D.
We have two functions, $f_1(i,j)$, $f_2(i,j)$ defined on the state space $\{(i,j) | ...
- 251
1
vote
1
answer
117
views
RSolve with integer and boolean variable
I have a recurrence relation with two variables $i, b$ where
$i \in \{0, \ldots, n-1\}$ for some parameter $n \in \mathbb{N}$; and $b\in \{0,1\}$.
I tried to solve it using RSolve, but the function ...
- 251
0
votes
0
answers
147
views
How to Solve this recurrence relation?
When I use RSolve[]
[![enter image description here][1]][1]
It would show this.
I want to solve it to a[n], the function of n & E
How to do that?
The original ...
- 23
3
votes
1
answer
167
views
How to use Manipulate with ListLinePlot
I'd like to run Manipulate with 0<r<=4 that preserves the ListLinePlot of the recurrence table given with the colors shown. I'm looking to use the autorun feature in Manipulate to show how the ...
- 1,773
0
votes
1
answer
65
views
Substitution of sequences to derive recursive mean
I would have the following derivation to calculate the recursive moving average and I'd like to follow it as closely as possible in Mathematica.
For the sequence where $y(i)$ is considered as an ...
- 437
4
votes
1
answer
131
views
How to solve for multiple (cascading) recurrence relations
I am working with recurrence relations with a simple base:
\begin{equation}
Y_i = aY_{i-1} + (1-a)X_i \quad \mbox{and if $Y_0=0$ then} \quad Y_n = (1-a)\sum_{i=1}^n a^{i-1} X_i \tag{1}
\end{equation}
...
- 165