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[3]}, 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

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

128 views

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: ...
136 views

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[0] := 1 a[n_] := Sqrt[3] + 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 ...
83 views

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146 views

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: ...