# Questions tagged [difference-equations]

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

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### Using RSolve to solve a recurrence relation

I am attempting to solve this recurrence relation. T[n] = n^(1.5) + T[n - 4] which I believe simplifies to n^(2.5) I ...
284 views

423 views

### Finding Hofstadter's Q-Sequence very slow

I'm trying to find Hofstadter's Q-Sequence. I tried: RSolve[{Q[n] == Q[n - Q[n - 1]] + Q[n - Q[n - 2]], Q == 1, Q == 1}, Q[n], n] but it doesn't work. ...
318 views

### Plotting system of recursive sequences [duplicate]

If I have a system of recursive sequences like x[n+1]=2x[n]+5(y[n])^2 y[n+1]=.5x[n]-3(y[n])^2 How can I plot it as a curves ...
179 views

### Improving my method for solving iterative algebraic equations

So I wish to solve the following $i$ equations for $\eta_i$ $$p(x)+\rho_i z_i + \frac{(u_id)^2}{2(\eta_{i-1}(x)-\eta_i(x))^2}+\rho_i \eta_i(x) = B_i$$ where we have the following definitions and $x$ ...
567 views

### Solving recurrent function with 2 variables

My understanding of Mathematica is very limited since I just started using it, I would appreciate any feed back or help. I am trying to find the closed form of a recurrent function with 2 variables: ...
181 views

### Is RSolve capable of solving the following functional equation? [closed]

I would like to use RSolve (or some other method) to solve the following functional equation: ...
86 views

### Simple linear 2nd order difference equation

I'm trying to run the following code. Unfortunately, there's a mistake in it, which I can't find. Can anyone of you help me? I guess it's very simple. Thanks so much in adavance! ...
125 views

### Problem with using RSolve to solve recurrence equations

Whenever I run the my code, the output of Mathematica is only a copy of the input again. ...
114 views

### How can MovingAverage be used for the solution of nd solve?

The code I used is as below but it doesn't work. Is there anyone who could understand and solve the problem? I want to plot d instead of s.Also, How can I fit a linear function to the d'. ...
150 views

### first order pde [closed]

I wrote below code to solve a first order partial differential equation and find $p(k,t)$ ...
96 views

### RecurrenceTable with vectors

Is there a way to call parts of a vector in RecurrenceTable? This does not work: ...
51 views

### What is the natural sequence of commands to apply RSolve to a DifferenceRoot[Function? [duplicate]

I am generating some DifferenceRoot[Functions, but to apply RSolve to them, I'm just doing some cutting and pasting from the ...
116 views

### Are there different Method options that can be used with FindSequenceFunction?

The help page states that Method is an option to use with FindSequenceFunction, but I don't find any further information. (There ...
114 views

### How can I express chains of filters using recurrence relations?

Here's example of what I would typically do in Python to play around with system of custom filters: ...
507 views

### How do I recursively calculate this equation and generate a list of iteration?

How do I write a recursive equation to compute a list of answers? I tried NestList, but it didn't work. ...
82 views

### Weird RecurrenceTable bug

The output of RecurrenceTable seems to lose a level when there are more than 250 points and one variable. Easiest to explain with an example: Good: ...
237 views

### Solving a nonlinear recurrence equation

How to solve the following nonlinear recurrence equation using RSolve? $$a(n+1):=\frac{1-(1-a(n)^4)^{1/4}}{1+(1-a(n)^4)^{1/4}} , \quad a(0):=\sqrt{2}-1$$ I tried: ...
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### Equivalent different-order difference equations--implications, if any?

I have a sequence of rational values. If I apply the FindSequenceFunction command to the first 48 (but no fewer) I get the result ...
347 views

### RecurrenceTable iteration variable not localized? Bug or user error?

I recently lost a lot of time on this and need to understand whether I have misunderstood MMA operations or there's a problem. I am using MMA 10.1 on Windows 7 64-bit. The essence of the issue is ...
451 views

### plotting and manipulate plot for logistic model (recursive function)

For a larger project on chaos, I am trying to write a short program that graphs the logistic model with different constant values, in this case the constant being "r". A) Is there a way to use Table ...
558 views

### How to simplify output of Series?

The command Series[Sum[Sum[1/(a*b), {b, a, 3 a}], {a, 1, N/Sqrt}, Assumptions -> N > 0], {N, Infinity, 1}] produces a somewhat complicated answer <...
402 views

### Solving a system of recurrence relations using Mathematica

Can Mathematica solve (for b[k] and c[r]) the following system of recurrence relations? b[k] ...
269 views

### Find RSolve solution reflecting special structure of DifferenceRoot[Function[{\[FormalY], \[FormalN]}

RSolve yields a large (multi-page) solution (LeafCount=25891) containing a number of 7F6 (and higher) hypergeometric functions when applied to ...
444 views

### Can I simplify (solve) a certain DifferenceRoot expression?

I've generated this expression ...
103 views

### How to replace the symbol n in DifferenceRoot

I'd like to employ another symbol (say alpha or k) instead of n in the following (type of) ...
203 views

### Incorrect answer given by RSolve

Bug introduced in 9.0 or earlier and persisting through 11.0.1 or later Also posted in Wolfram Community. I tried to solve the following nonlinear recurrence relation using ...
320 views

### Sampling a continuous function to create sequence of discrete values

My question is straightforward: How do I convert a continuous function into a discrete-valued function? The function I want to convert is the JacobiAmplitude function: ...
99 views

### solving a non linear (log-linear) recurrence relation

I'd like to solve the recurrence relation \begin{align*} f(n+1) &= 2 f(n)^2 h(n) \\ h(n+1) &= h(n) f(n) \\ f(2) & = h(2) = 2 \end{align*} for an explicit solution for $h$ and $f$. So ...
1k views

### Finite difference method not converging to correct steady state or conserving area?

I am working with the following PDE, which is an advection-diffusion type equation. It describes the movement of a fluid-fluid interface inside an annulus of inner radius $R_1$ and outer $R_2$ under ...
287 views

### Lyapunov Exponent as a function of parameter

I am working at Rossler system and I would like to ask you for some help. This system is described by equations: \begin{array}{ll} \dot{x} = -y - z \\ \dot{y} = x + 0.2y \\ \label{eq:UkladRosSP} \dot{...
639 views

### Solving Recurrence Equation $a_{n+1}=a_n(1-a_n)$

How to solve following recurrence equation $$a_0=2$$ $$a_{n+1}=a_n(1-a_n)$$ I tried: ...
99 views

### Solving recurrence equation depending on a parameter

I have a recurrence relation which depends on a parameter $t$ and I am trying to solve it using RSolve. This is what I typed: ...
338 views

### Dynamical system problem x(t+1) = Ax(t)

I have a problem that have been trying to solve but it's not going so good. I would like some guidelines on how to work myself around this problem: Two neighboring countries spy on each other and ...