# Questions tagged [difference-equations]

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

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### Problem with RSolve function

When I use RSolve to solve the recurrence: $S(n)=\dfrac{1}{-S(n-1)-2},S(1)=-2/3$, it gives an empty solution: however the solution should be:$S(n)=-\dfrac{n+1}{n+2}$ Did I do something wrong?
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### 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. ...
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### Error when Solving Recurrence Relation

I would like to analyze the following recurrence relation. $r_i = r_{i-1} - \frac{1}{2} \cdot \sqrt{1 - \frac{4\pi^2\cdot r_{i-1}^2}{n^2}}$ $r_0 = \frac{n}{2\pi}$ I have implemented this as ...
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### DifferenceRoot help

I have being calculate some Series Coefficient and the result was and DifferenceRoot equation but i do not how ...
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### Generating DifferenceRoot Equation

I like to find a difference root equation I use the following methods use for mathematica but I have not get any result Clear[p] ...
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### Discrete-time Lyapunov exponent plot

I am trying to create a Lyapunov exponent plot as a function of $\alpha$ for two functions: $$f(x) = (\alpha + 1)x - \alpha x^{3}$$ and a piecewise function given by following Mathematica code: <...
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### Using rule output as function

Im trying to define a function using the output from RSolve, however i cant get it to work properly. I have a RSolve that output something like: ...
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### RSolve and a Piecewise Recurrence + Runtime

This should really be a comment to this answer but I don't have enough rep. I'd like to know how to do the same thing (efficiently - see below) but with $\mod 3$ conditions, i.e. define a[k] to be the ...
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### RSolve for three arguments

I would like to find the general expression for a recursive equation: ...
160 views

### Recurrence Relation with two variables and boundary conditions

I try to express the following recurrence relation in Mathematica: I am very sorry but for any reason I am not allowed to embed math code here... \begin{align*} x_{1,t} &= \frac{1}{2} x_{1,t-...
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### Solution of differential equation and then draw a graph

I have two differential equations: $da/dt = a (.3 a^{-3} + .7)^{1/2}$ and $d \tau /dt = 1/a$. The initial conditions are $t = 0$; $a = 1$ and $\tau = 0$, respectively. How can I solve the ...
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### Using NIntegrate in Finite Difference Derivative method

I'm trying to solve a second order differential equation using the code given by @xzczd here which is based on this. What this ...
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### Zeros of a rational fraction sequence

This is a follow-up of the question Finding a function/differential equation from a 2nd order recurrence relation, I asked yesterday. The reason why I didn't edit the original question was that in ...
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### Solving a boundary-value recurrence relation

I would like to solve a recurrence relation of the form ...
### How many solutions are there in this equation $u_{2018}=0$?
I have a sequence $(u_n)$ so that $u_1=a$ and $u_{n+1}=4u_n (1-u_n)$, for all $n=1,2,\ldots$. How many solutions are there in this equation $u_{2018}=0$? I tried ...