# Questions tagged [difference-equations]

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

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108 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: ...
498 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. ...
80 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: ...
205 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: ...
84 views

### 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 ...
322 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 ...
413 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 ...
525 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 <...
376 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] ...
263 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 ...
384 views

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

I've generated this expression ...
101 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) ...
197 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 ...
302 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: ...
86 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 ...
983 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 ...
240 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{...
543 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: ...
92 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: ...
327 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 ...
401 views

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### Making a table or expression based on previous values

I would like to illustrate rational expectations based on the following equation p[[t+1]] == 1/(1 - ψ (β - 1)) m[[t+1]] - ψ (β - 1)/(1 - ψ (β - 1)) p[[t]] by ...
210 views

### How to solve this recursive system?

I try to solve the equation system as ...
331 views

### Two dimensional recurrence

My actual problem is a bit more complicated, but let us first assume that we have a recurrence relation of the following type $a_{n,l} = a_{n-1,l} + a_{n-1,l-1} + a_{n,l-1}$ The boundary is given, ...
126 views

### How can I find the coefficients of the next recursive symbolic function?

I have the following function $$f(x+3k) = -mf(x+2k)+f(x)$$. If we get $x=x+k$, then $$f(x+4k) = -mf(x+3k)+f(x+k) = m^2f(x+2k)+f(x+k)-mf(x)$$. Also we obtain the coefficients of the final functions,...
50 views

### Recursions where one definition depends on another. How to Block or have local variables?

I have been using Mathematica to solve a second order differential equation using the second order Verlet method. My code looks like: ...
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### How to find negative numbers for my recurrence formula?

The generalized recurrence formula is F[n_]:=F[n]=F[n-1]+F[n-p-1]; with the initial conditions ...
1k views

### Limit n->Infinity of recursive sequence

I have defined a recursive sequence a := 1 a[n_] := Sqrt + 1/2 a[n - 1] because I want to calculate the Limit for this ...
313 views

### Finite Difference - heat generation in a square (square within a square)

I am trying to develop a code that will allow me to solve the following problem. Lets say that I have a square block, inside that square block I have a smaller square box thats at a certain ...
292 views

### Evolution of a trait in an asexual population (performance tuning)

I just coded a simple simulation module that looks at the evolution of a continuous trait in a haploid asexually reproducing population under density dependent competition in discrete time (i.e. non-...
159 views

### How do I use RSolve to solve the problem below?

RSolve can't compute the solution. Appears that Mathematica is having a convergence problem. I don't know if the boundary conditions are properly defined... ...
461 views

### Recursion question

The first two terms of a sequence are $a_1 = 1$ and $a_2 = \frac {1}{\sqrt3}$. For $n\ge1$, $$a_{n + 2} = \frac {a_n + a_{n + 1}}{1 - a_na_{n + 1}}.$$ What is $|a_{2009}|$? So I tried (thanks to ...
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### Kernel crash when evaluating NDSolveValue

I had a code that was working fine and I tried to add an extra few lines to find the solution of the same equation with different conditions. The original NDSolveValue solutions work fine but when it ...
788 views

### Partial differential equation, Finite difference Method

For my research project I am trying to solve following partial differential equation in Mathematica (V[r]*ψ[u, v])/4 + Derivative[1, 1][ψ][u, v] == 0 with ...
562 views

### Show Factorial instead of Gamma in the result of RSolve

Now I wanted to solve for a recurring function with RSolve. Here's how I tried: ...