# Questions tagged [difference-equations]

Tag for the usage of RSolve, RecurrenceTable, DifferenceRoot, and other functions related to difference equations.

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### Sigma Delta Modulator in Mathematica

Below code is for 1st order sigma delta modulator used in ADC/DAC circuits. ...
343 views

### 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 ...
86 views

### Recursion not working

I am trying to find the terms x7,x8,x9 and so on from the recursive relation given in the code. ...
96 views

### How to solve recurrence equation using RSolve?

How can I solve the following recurrence equation while I dont have the initial values? Is it possible to solve this using RSolve? ...
127 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 ...
142 views

86 views

### RecurrenceTable two difference equations

I have tried to use RecurrenceTable to Solve a system of two differential equations. I look for having a sequence of the two variables n (population growth factor) and w (wages). I have provided ...
150 views

### Solving logarithmic 2D Nonlinear GPE Equation

I am trying to solve the logarithmic 2D Nonlinear GPE Equation from this paper https://arxiv.org/pdf/1801.10274.pdf. But failed to get the ground state solution and vortices. I tried to solve in ...
144 views

### RSolve returns a wrong result, why?

I'm trying to solve the following recurrence relation: $\begin{cases} u_{0} = a \\ u_{n + 1} = - \sum_{i = 0}^{n} u_{i} u_{n - i} \end{cases}$ Here is my Mathematica code: ...
223 views

### Stability classification code for dynamic system

I'm interested in carrying out stability analysis on discrete dynamic systems, as was done in this paper. The Author used their function ...
1 vote
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### Progress Indication for RecurrenceTable

I am trying to figure out how to implement progress indicator in RecurrenceTable. I have a complicated code within the With function that contains recurrence table. A simple code will suffice say, <...
116 views

### problem in plotting phase portrait t for nonlinear system of difference equation

I have tried to do a code about phase portrait plot for this system of difference equation: \begin{align} x_{t+1} &= ax_{t}^2+y_t+1 \\ y_{t+1} &= bx_t^2-1 \end{align} I took 'a=0.5','b=2' but ...
1 vote
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### RecurrenceTable with multiple vectors

I am trying to do numerical calculations by recursion with vectors. I wrote a test code with single variable using 2 ODE's as shown below, ...
104 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? ...
52 views

### RSolve[] gives error RSolve::litarg when solving demo equations from the official documentation

The official documentation of RSolve[] (specifically, in the fifth paragraph of the seciton "Details and Options") states that: The specification a∈Vectors[m] or a∈Matrices[{m,p}] can be ...
1 vote
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### RSolve with two boundary conditions

I want to solve a recurrence equation that has boundary conditions on both sides: $a= 1$ $a[n]= 10$ $a[i] = a[i-1]-a[i+1]\quad \forall i \in \{1, \ldots, n-1\}$ This should be a well defined ...
67 views

### 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 [...
1 vote
301 views

### How to plot the "trapping region" in Henon Map?

I am writing a paper that makes use of the Henon map. I have managed to plot the Henon map but now require plotting the "trapping region" shown in the image. Do I require to plot it as a ...
89 views

### Inverse of an Animation

I was thinking, it's possible to plot inverse an animation?? ...
88 views

### Difference between NDSolve and RecurrenceTable

I have the following system which I model as difference equations and solve with RecurrenceTable: ...